Understand Functions: CCSS.Math.Content.8.F.A.1 - Common Core: 8th Grade Math
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Solve the equation:
Solve the equation:
To solve the quadratic equation, 
, we set the equation equal to zero and then factor the quadratic, 
. Because these expressions multiply to equal 0, then it must be that at least one of the expressions equals 0. So we set up the corresponding equations 
and 
to obtain the answers 
and 
.
To solve the quadratic equation,
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Solve for 
:
Solve for
To factor this equation, first find two numbers that multiply to 35 and sum to 12. These numbers are 5 and 7. Split up 12x using these two coefficients:
To factor this equation, first find two numbers that multiply to 35 and sum to 12. These numbers are 5 and 7. Split up 12x using these two coefficients:
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Which of the following equations represents a one-to-one function:
Which of the following equations represents a one-to-one function:
Only equation B maps each value of 
into a unique value of 
and in a similar way each and every value of 
maps into one and only one value of 
.
Only equation B maps each value of
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Find 
.
Find
This question demonstrates that complicated functions are not complicated at every point.
To solve the function at x=1, all that is necessary is familiarity with the operations used.
This question demonstrates that complicated functions are not complicated at every point.
To solve the function at x=1, all that is necessary is familiarity with the operations used.
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Solve for 
:
Solve for
To find 
, we must factor the quadratic function:
To find
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Solve for 
:
Solve for
To find 
, we want to factor the quadratic function:
To find
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Define 
.
Evaluate 
.
Define
Evaluate
To evaluate 
substitute six in for every x in the equation.
To evaluate
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Define 
Which of the following is equivalent to 
?
Define
Which of the following is equivalent to
To solve this problem replace every x in 
with 
.
Therefore,
To solve this problem replace every x in
Therefore,
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Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above
Select the table that properly represents a function.
Select the table that properly represents a function.
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Each of the tables provided contains sets of ordered pairs. The input column represents the x-variables, and the output column represents the y-variables. We can tell if a set of ordered pairs represents a function when we match x-values to y-values.
In order for a table to represents a function, there must be one and only one input for every output. This means that our correct answer will have all unique input values:
Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:
Compare your answer with the correct one above