﻿ Function Worksheets - Page 11 | Problems & Solutions

Function Worksheets - Page 11

Function Worksheets
• Page 11
101.
What is the value of the function $f$(9), if $f$($x$) = 3$x$ + 5?
 a. 10 b. 32 c. 54 d. 22

Solution:

f(x) = 3x + 5
[Original equation.]

f(9) = 3(9) + 5
[Substitute 9 for x.]

= 32
[Simplify.]

102.
Choose the equation that satisfies the input - output table.
 Input($x$) 0 1 2 3 4 5 Output($y$) 50 54 58 62 66 70
 a. $y$ = 50 - 5$x$ b. $y$ = 50 + 4$x$ c. $y$ = 50 + 6$x$ d. $y$ = 50 - 7$x$

Solution:

y = 50 - 5x
[Consider choice A.]

y = 50 - 5(0) = 50
[Substitute 0 for x.]

y = 50 - 5(1) = 45
[Substitute 1 for x.]

In the table for x = 1, y = 54. So, first equation is ruled out.

y = 50 + 4x
[Consider choice B.]

y = 50 + 4(0) = 50
[Substitute 0 for x.]

y = 50 + 4(1) = 54
[Substitute1 for x.]

y = 50 + 4(2) = 58
[Substitute 2 for x.]

y = 50 + 4(3) = 62
[Substitute 3 for x.]

y = 50 + 4(4) = 66
[Substitute 4 for x.]

y = 50 + 4(5) = 70
[Substitute 5 for x.]

The equation y = 50 + 4x satisfies the table.

103.
The table represents the relationship between $x$ and $y$.
 $x$ - 1 1 2 3 $y$ 5 7 8 9

Which of these equations best represents the relationship?
 a. $y$ = $x$ + 6 b. $y$ = 2$x$ + 4 c. $y$ = - $x$ - 5 d. $y$ = 3$x$ + 3

104.
Identify an equation that represents the rule for the pattern shown in the table.
 $x$ 3 5 7 9 $y$ 18 20 22 24

 a. $y$ = 3$x$ + 1 b. $y$ = 6$x$ c. $y$ = 4$x$ d. $y$ = $x$ + 15

105.
Which of the equations best represents the rule for the table?
 $x$ 1 2 3 4 $y$ 8 16 24 32

 a. $y$ = 8$x$ b. $y$ = 3$x$ + 7 c. $y$ = $x$ + 7 d. $y$ = 8$x$ + 5

106.
Rebecca is staying as a paying guest in her aunt's house. Her aunt charges her $20 per month as rent and$15 per day for food. The total cost $c$ = 20 + 15$n$, $n$ represents the number of days she had her food in her aunt's house. Which of the tables best suits the equation?

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

Solution:

c = 20 + 15n
[Original equation.]

c = 20 + 15(0)
[Replace n with 0.]

= 20
[Simplify.]

c = 20 + 15(1)
[Replace n with 1.]

= 35
[Simplify.]

c = 20 + 15(2)
[Replace n with 2.]

c = 50
[Simplify.]

c = 20 + 15(3)
[Replace n with 3.]

c = 65
[Simplify.]

c = 20 + 15(4)
[Replace n with 4.]

= 80
[Simplify.]

c = 20 + 15(5)
[Replace n with 5.]

= 95
[Simplify.]

The input and output values of table-1 matches with the results of the equation.

Table-1 satisfies the equation.

107.
Which of the tables represents the equation $y$ = 3(4$x$ + 12) for $x$ = 0, 1, 2, 3, 4, 5?

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

Solution:

y = 3(4x + 12)
[Original equation.]

y = 3[4(0) +12] = 36
[Replace x with 0.]

y = 3[4(1) + 12] = 48
[Replace x with 1.]

y = 3[4(2) +12] = 60
[Replace x with 2.]

y = 3[4(3) +12] = 72
[Replace x with 3.]

y = 3[4(4) + 12] = 84
[Replace x with 4.]

y = 3[4(5) +12] = 96
[Replace x with 5.]

For the values of x, the corresponding values of y are 36, 48, 60, 72, 84 and 96.

So, Table 4 best suits the equation y = 3(4x + 12).

108.
Which equation satisfies the input-output table?
 Input($x$) 0 1 2 3 4 5 Output($y$) 30 25 20 15 10 5
 a. $y$ = 30 - 6$x$ b. $y$ = 30 - 5$x$ c. $y$ = 30 - 7$x$ d. $y$ = 30 - 8$x$

Solution:

y = 30 - 6x
[Consider choice A.]

y = 30 - 6(0) = 30
[Replace x with 0.]

y = 30 - 6(1) = 24
[Replace x with 1.]

In the table for x = 1, y = 25. So first equation is ruled out.

y = 30 - 5x
[Consider choice B.]

y = 30 - 5(0) = 30
[Replace x with 0.]

y = 30 - 5(1) = 25
[Replace x with 1.]

y = 30 - 5(2) = 20
[Replace x with 2.]

y = 30 - 5(3) = 15
[Replace x with 3.]

y = 30 - 5(4) = 10
[Replace x with 4.]

y = 30 - 5(5) = 5
[Replace x with 5.]

The equation y = 30 - 5x satisfies the table.

109.
A function $y$ = 8$x$ represents a line passing through the origin. If $x$ ≥ 0 and $x$ ≤ 5, then which table shows the relation between input and output for the function?

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

Solution:

As, x ≥ 0 and x ≤ 5, x takes the values between 0 and 5 including 0 and 5.

y = 8x
[Original equation.]

y = 8(0) = 0
[Replace x with 0.]

y = 8(1) = 8
[Replace x with 1.]

y = 8(2) = 16
[Replace x with 2.]

y = 8(3) = 24
[Replace x with 3.]

y = 8(4) = 32
[Replace x with 4.]

y = 8(5) = 40
[Replace x with 5.]

The values of y for the corresponding values of x are 0, 8, 16, 24, 32, and 40.

Table 1 satisfies the equation.

110.
Which of the graphs best suits the equation $f$($x$) = 2$x$ - 1?

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

Solution:

f(x) = 2x - 1
[Original equation.]

f(0) = 2(0) - 1
[Replace x with 0.]

f(0) = - 1
[Simplify.]

f(1) = 2(1) - 1
[Replace x with 1.]

f(1) = 1
[Simplify.]

f(2) = 2(2) - 1
[Replace x with 2.]

f(2) = 3
[Simplify.]

Among the choices, graph 3 suits the equation.