Identifying Graphs & Effects of Function Manipulation: CCSS.Math.Content.HSF-BF.B.3 - Common Core: High School - Functions
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Given the function 
identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function 
creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function 
.
The function 
in the graph above has a 
-intercept at zero.
Step 2: Use technology to graph the new function 
.
The function 
in the graph above has a 
-intercept at three.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function 
, the graphically effect 
creates is a vertical shift upwards of three units.
Step 4: Answer the question.
In other words, 
moves the original function 
up three units.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at negative two.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a vertical shift down of two units.
Step 4: Answer the question.
In other words, 
moves the original function down two units.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
.
The function 
in the graph above has a -intercept at four.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a vertical shift upwards of four units.
Step 4: Answer the question.
In other words, 
moves the original function up four units.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at negative five.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a vertical shift down of five units.
Step 4: Answer the question.
In other words, 
moves the original function down five units.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at one and the vertex is moved to the right one unit.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a phase shift to the right one unit.
Step 4: Answer the question.
In other words, 
moves the original function right one unit.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at one and the vertex is moved to the left one unit.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a phase shift to the left one unit.
Step 4: Answer the question.
In other words, 
moves the original function left one unit.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at four and the vertex is moved to the left two unit.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a phase shift to the left two units.
Step 4: Answer the question.
In other words, 
moves the original function left two units.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at nine and the vertex is moved to the right three units.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function , the graphically effect 
creates is a phase shift to the right three units.
Step 4: Answer the question.
In other words, 
moves the original function right three units.
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Given the original function
Step 4: Answer the question.
In other words,
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at zero and the graph narrows.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
narrows the original function 
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at zero and the graph widens.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
widens the original function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at zero and the graph narrows.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
narrows the original function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
Compare your answer with the correct one above
Given the function identify the graphically effect 
creates.
Given the function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function creates.
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function .
The function in the graph above has a -intercept at zero.
Step 2: Use technology to graph the new function 
The function 
in the graph above has a -intercept at zero and the graph widens.
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
widens the original function
This question is testing one's ability to identify the graphically transformation that algebraic manipulation to the function
For the purpose of Common Core Standards, "Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k ." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.3).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Use technology to graph the function
The function
Step 2: Use technology to graph the new function
The function
Step 3: Compare and interpret the two graphs to identify the graphically effect.
When the two functions are plotted on the same graph where the original function is in blue and the shifted function is in orange is below.
Step 4: Answer the question.
Compare your answer with the correct one above