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Graph Linear Functions Worksheet - Page 12

Graph Linear Functions Worksheet
  • Page 12
 111.  
If the function f(x) = - 15x - 10, then what is the value of f(-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


Correct answer : (3)
 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.


Correct answer : (3)
 113.  
Which of the following is a linear function?
a.
y = 1 x + 3
b.
y = 3x + 2
c.
y = 3x2
d.
y = 3x2 + 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.


Correct answer : (2)
 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.]


Correct answer : (1)
 115.  
Which of the following is a linear function?
a.
y = 1 x
b.
y = x + 9
c.
y = x2 + 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.


Correct answer : (2)
 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.


Correct answer : (3)
 117.  
Which of the following is a linear function?
a.
y2 = 1 x + 2
b.
y = 2(x - 4) + 10
c.
y = x2 - 4
d.
y = x3 + 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.


Correct answer : (2)
 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.


Correct answer : (4)
 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.


Correct answer : (1)
 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.


Correct answer : (3)

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