Understand Functions: CCSS.Math.Content.8.F.A.1

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8th Grade Math › Understand Functions: CCSS.Math.Content.8.F.A.1

Questions 1 - 10
1

Select the table that properly represents a function.

Screen shot 2016 03 14 at 10.16.55 am

Screen shot 2016 03 14 at 10.17.07 am

Screen shot 2016 03 14 at 10.17.29 am

Screen shot 2016 03 14 at 10.18.00 am

Explanation

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:

Screen shot 2016 03 14 at 10.16.55 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 10.17.17 am

Screen shot 2016 03 14 at 10.17.39 am

Screen shot 2016 03 14 at 10.18.12 am

2

Find .

Undefined

Explanation

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.

3

Select the table that properly represents a function.

Screen shot 2016 03 14 at 10.42.22 am

Screen shot 2016 03 14 at 10.17.07 am

Screen shot 2016 03 14 at 10.11.25 am

Screen shot 2016 03 14 at 10.07.30 am

Explanation

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:

Screen shot 2016 03 14 at 10.42.22 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 10.17.17 am

Screen shot 2016 03 14 at 10.11.39 am

Screen shot 2016 03 14 at 10.07.43 am

4

Select the table that properly represents a function.

Screen shot 2016 03 14 at 10.36.09 am

Screen shot 2016 03 14 at 8.52.16 am

Screen shot 2016 03 14 at 9.44.51 am

Screen shot 2016 03 14 at 9.55.39 am

Explanation

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:

Screen shot 2016 03 14 at 10.36.09 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 8.52.56 am

Screen shot 2016 03 14 at 9.45.07 am

Screen shot 2016 03 14 at 9.55.50 am

5

Define

Which of the following is equivalent to ?

Explanation

To solve this problem replace every x in with .

Therefore,

6

Select the table that properly represents a function.

Screen shot 2016 03 14 at 9.54.52 am

Screen shot 2016 03 14 at 9.56.08 am

Screen shot 2016 03 14 at 9.56.36 am

Screen shot 2016 03 14 at 9.55.39 am

Explanation

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:

Screen shot 2016 03 14 at 9.54.52 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 9.55.50 am

Screen shot 2016 03 14 at 9.56.24 am

Screen shot 2016 03 14 at 9.56.49 am

7

Solve the equation:

Explanation

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 .

8

Solve for :

Explanation

To find , we want to factor the quadratic function:

9

Which of the following equations represents a one-to-one function:

Explanation

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 .

10

Select the table that properly represents a function.

Screen shot 2016 03 14 at 10.07.20 am

Screen shot 2016 03 14 at 10.07.30 am

Screen shot 2016 03 14 at 10.08.00 am

Screen shot 2016 03 14 at 10.11.25 am

Explanation

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:

Screen shot 2016 03 14 at 10.07.20 am

Functions cannot have more than one input value that is the same; thus, the following tables do not represent a function:

Screen shot 2016 03 14 at 10.07.43 am

Screen shot 2016 03 14 at 10.08.13 am

Screen shot 2016 03 14 at 10.11.39 am

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