Construct Linear and Exponential Functions, Arithmetic and Geometric Sequences: CCSS.Math.Content.HSF-LE.A.2 - Common Core: High School - Functions

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Question

What is the function that describes the following graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=2$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The red lines in the below graph represent the slope.

The rise is three units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{1-0}=\frac{3}{1}=3$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The red lines in the below graph represent the slope.

The rise is two units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{1-0}=\frac{2}{1}=2$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{0--1}{1-0}=\frac{1}{1}=1$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is three units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2--1}{1-0}=\frac{3}{1}=3$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is two units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{1-0}=\frac{2}{1}=2$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is four units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{1-0}=\frac{4}{1}=4$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is two units to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{2-0}=\frac{1}{2}$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

$y=\frac{1}{2}x$

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-2$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1--2}{1-0}=\frac{1}{1}=1$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-3$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is three units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{0--3}{1-0}=\frac{3}{1}=3$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is two units to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{2-0}=\frac{1}{2}$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

$y=\frac{1}{2}x+1$

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is three units up and the run is four units to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{4-0}=\frac{3}{4}$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

$y=\frac{3}{4}x$

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=2$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit down and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{1-0}=\frac{-1}{1}=-1$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

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