﻿ Graph Linear Functions Worksheet - Page 12 | Problems & Solutions

# Graph Linear Functions Worksheet - Page 12

Graph Linear Functions Worksheet
• Page 12
111.
If the function $f$($x$) = - 15$x$ - 10, then what is the value of $f$($\frac{-1}{3}$ )?
 a. -10 b. -5 c. None of the above

#### Solution:

f(x) = -15x -10
[Original equation.]

f(-1 / 3) = -15 (-1 / 3) - 10
[Substitute -1 / 3 for x.]

f(-1 / 3) = 5 - 10
[Simplify.]

So, f(-1 / 3) = -5

112.
Identify the function the graph represents.

 a. Quadratic function b. Non-linear function c. Linear function d. None of the above

#### Solution:

The line in the graph represents a function with positive slope and a y-intercept.

The general equation for the graph is y = mx + c.

So, the line in the graph represents a linear function.

113.
Which of the following is a linear function?
 a. $y$ = $\frac{1}{x}$ + 3 b. $y$ = 3$x$ + 2 c. $y$ = 3$x$2 d. $y$ = 3$x$2 + 3

#### Solution:

A function which is in the form of f(x) = mx + c is called a linear function.

In the choices y = 3x + 2 is in the form of f(x) = mx + c.
[m = 3 and c = 2.]

So, the function in choice B is a linear function.

114.
What function does the equation $f$($x$) = - $x$ + 5 represent?
 a. Linear function b. Quadratic function c. Non-linear function

#### Solution:

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

The equation is in the form of f(x) = mx + c.
[m = -1 and c = 5.]

So, the equation represents a linear function.
[An equation in the form of f(x) = mx + c is called a linear function.]

115.
Which of the following is a linear function?
 a. $y$ = $\frac{1}{x}$ b. $y$ = $x$ + 9 c. $y$ = $x$2 + $\frac{1}{5}$ d. $y$ = ($x$ + 3)3

#### Solution:

Consider the choice A, y = 1 / x.

This can also be written as y = x-1, which is not a linear function.

Consider the choice B, y = x + 9.

The equation is in the form of y = mx + c, which is a linear function.

So, choice B is a linear function.

116.
Which of the following is not a linear function?
 a. $f$($x$) = -$x$ b. $f$($x$) = $x$ + 3 c. $f$($x$) = √$x$ + 3 d. None of the above

#### Solution:

A function in the form of f(x) = mx + c is called a linear function.
[In a linear function, the exponent of x must be 1.]

Among the choices f(x) = √x + 3 is not in the form of a linear function.
[The exponent of x is 1 / 2.]

So, the equation in choice C is not a linear function.

117.
Which of the following is a linear function?
 a. $y$2 = $\frac{1}{x}$ + 2 b. $y$ = 2($x$ - 4) + 10 c. $y$ = $x$2 - 4 d. $y$ = $x$3 + 2

#### Solution:

A function which is in the form of f(x) = mx + c is called a linear function.

In the choices y = 2(x - 4) + 10 is in the form of f(x) = mx + c.

y = 2x - 8 + 10
[Original equation.]

y = 2x + 2
[m = 2 and c = 2.]

So, the function in choice B is a linear function.

118.
Which of the graphs best suits the function rule $y$ = $x$ + 2?

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

#### Solution:

y = x + 2
[Original equation.]

y = - 2 + 2
[Substitute - 2 for x.]

= 0
[Simplify.]

y = - 1 + 2
[Substitute - 1 for x.]

= 1
[Simplify.]

y = 0 + 2
[Substitute 0 for x.]

y = 2
[Simplify.]

Graph 4 satisfies the function rule.

119.
Which of the graphs best suits the equation $y$ = - $x$?

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

#### Solution:

y = - x
[Original equation.]

y = - (- 2) = 2
[Substitute x = - 2.]

y = - (- 1) = 1
[Substitue x = - 1.]

y = 0
[Substitue x = 0.]

y = - 1
[Substitue x = 1.]

y = - 2
[Substitue x = 2.]

Among the choices, Graph 1 satisifes the condition.

120.
If $f$($x$) = 0.24($x$ + 2) + $x$ - 0.3, then find the value of $f$(2) and $f$(3).
 a. 6.66, 6.10 b. 1.66, 4.10 c. 2.66, 3.90 d. 4.66, 5.10

#### Solution:

f(x) = 0.24(x + 2) + x - 0.3
[Orginal equation.]

f(2) = 0.24(2 + 2) + 2 - 0.3
[Substitue 2 for x.]

= 2.66
[Simplify.]

f(4) = 0.24(3 + 2) + 3 - 0.3
[Substitue 3 for x.]

= 3.90
[Simplify.]

So, f(2) = 2.66 and f(3) = 3.90.