﻿ Function Worksheets | Problems & Solutions

# Function Worksheets

Function Worksheets
• Page 1
1.
Which table represents a function?

 a. Table A b. Table B c. Table C d. Table D

#### Solution:

Table A represents a function, since there is exactly one output for each input.

In Table B, the input value 20 has two output values.

In Table C, the input value 10 has two output values.

In Table D, the input value 40 has two output values.

So, Table B, C and D do not represent a function.

2.
Which of the line graphs represents the function given by the input-output table?

 a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4

#### Solution:

From the table, as x increases, y increases up to x = 1 and then as x increases y decreases from x = 1 to x = 5.

Graph 3 satisfies the table.

3.
Which table represents a function?

 a. Table A b. Table A & B c. Table A & C d. All

#### Solution:

In all the tables, there is exactly one output for each input.

So, all the tables represent a function.

4.
Choose an input-output table for the function $y$ = 2$x$ - 3, for $x$ = 5, 10, 15, 20, and 25.

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

 Input Function Output x = 5 y = 2(5) - 3 y = 7 x = 10 y = 2(10) - 3 y = 17 x = 15 y = 2(15) - 3 y = 27 x = 20 y = 2(20) - 3 y = 37 x = 25 y = 2(25) - 3 y = 47

So, the table for the function y = 2x - 3 matches with Table 2.

5.
Choose an input-output table for the function $y$ = 3(10 - $x$), for $x$ = 0, 2, 4, 6, and 8.

 a. Table B b. Table C c. Table D d. Table A

#### Solution:

 Input Function Output x = 0 y = 3(10 - 0) y = 30 x = 2 y = 3(10 - 2) y = 24 x = 4 y = 3(10 - 4) y = 18 x = 6 y = 3(10 - 6) y = 12 x = 8 y = 3(10 - 8) y = 6

6.
Which function has an output of $m$ = 32 for an input of $n$ = 10?
 a. $m$ = 3$n$ + 2 b. $m$ = 2$n$ + 3 c. $m$ = 3$n$ - 2 d. $m$ = 32$n$

#### Solution:

m = 3n - 2

m = 3(10) - 2 = 28
[Substitute n = 10.]

m = 3n + 2

m = 3(10) + 2 = 32
[Substitute n = 10.]

m = 2n + 3

m = 2(10) + 3 = 23
[Substitute n = 10.]

m = 32n

m = 32(10) = 320
[Substitute n = 10.]

So, m = 3n + 2 has the output of m = 32, for an input of n = 10

7.
Which function is best reprsented by the table?
 Input($x$) 1 2 3 4 5 Output($y$) 4 7 10 13 16
 a. $y$ = 3$x$ - 1 b. $y$ = 3$x$ + 2 c. $y$ = 2$x$ + 2 d. $y$ = 3$x$ + 1

#### Solution:

On observing the table, it is found that the output 4 = (3 × 1) + 1, 7 = (3 × 2) + 1, 10 = (3 × 3) + 1, 13 = (3 × 4) + 1, 16 = (3 × 5) + 1

So, the function is y = 3x + 1

8.
Which function is best represented by the table?
 Input($x$) 1 2 3 4 5 6 Output($y$) 10 20 30 40 50 60
 a. $y$ = 10($x$ + 1) b. $y$ = 20($x$ + 1) c. $y$ = 10$x$ d. $y$ = 10($x$ - 1)

#### Solution:

On observing the table, it is found that the output 10 = 1 × 10, 20 = 2 × 10, 30 = 10 × 3, 40 = 10 × 4, 50 = 5 × 10, and 60 = 6 × 10

So, the function is y = 10x.

9.
Choose the range of the function from the input-output table.
 Input($x$) 1 2 3 4 5 6 Output($y$) 6 15 20 10 8 1

 a. {1, 6, 2, 15, 3, 20} b. {6, 15, 20, 10, 8, 1} c. {1, 2, 3, 4, 5, 6, 6, 15, 20, 10, 8, 1} d. {1, 2, 3, 4, 5, 6}

#### Solution:

The collection of all output values is the range of the function.

So, the range of the function from the table is {6, 15, 20, 10, 8, 1}.

10.
Katie had $8 with her. She sold $n$ apples at$4 each and earned some money. Identify an equation for the money $f$($n$) she had with her finally.
 a. $f$($n$) = 4$n$ + 8 b. $f$($n$) = 4 $n$ - 8 c. $f$($n$) = 8 - $n$ d. $f$($n$) = 8 $n$

#### Solution:

The money she had finally = money earned by selling n apples + money she had initially.

The money earned by selling n apples = n × cost of each apple = n × 4 = \$4n

So, the equation for the total money she had finally is f(n) = 4n + 8