# Nonlinear Function Worksheet

Nonlinear Function Worksheet
• Page 1
1.
Which of the graphs represents the function $f$($x$) = $\frac{6}{x}$, for $x$ = 1, 2, 3, 4?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 6x
[Original equation.]

f(1) = 61
[Substitute 1 for x.]

= 6
[Simplify.]

f(2) = 62
[Substitute 2 for x.]

= 3
[Simplify.]

f(3) = 63
[Substitute 3 for x.]

= 2
[Simplify.]

f(4) = 64
[Substitute 4 for x.]

= 1.5
[Simplify.]

Graph 2 satisfies the solution.

2.
Which of the graphs represents the function $f$($x$) = $\frac{60}{x}$, for $x$ = 4, 5, 6, 10, 12 and 15?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 60x
[Original equation.]

f(4) = 604 = 15
[Substitute the value of x = 4.]

f(5) = 605 = 12
[Substitute the value of x = 5.]

f(6) = 606 = 10
[Substitute the value of x = 6.]

f(10) = 6010 = 6
[Substitute the value of x = 10.]

f(12) = 6012 = 5
[Substitute the value of x = 12.]

f(15) = 6015 = 4
[Substitute the value of x = 15.]

Graph 1 represents the function f(x) = 60 / x.

3.
Which of the graphs represents the function $f$($x$) = 2$x$2 , for the values of $x$ = 0, 1, 2 and 3?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 2x2
[Original equation.]

f(0) = 2(0)2
[Substitute 0 for x.]

= 0
[Simplify.]

f(1) = 2(1)2
[Substitute 1 for x.]

= 2
[Simplify.]

f(2) = 2(2)2
[Substitute 2 for x.]

= 8
[Simplify.]

f(3) = 2(3)2
[Substitute 3 for x.]

= 18
[Simplify.]

Graph 2 satisfies the equation.

4.
Mike left his home and drove to his parents' house, which is 400 miles away. The function $f$($x$) = $\frac{400}{x}$ relates the time, $x$, (in hours) for his journey to the speed (in miles per hour). Which of the graphs represents the function?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 400x
[Original equation.]

f(x) = 4001
[Speed for 1 hour.]

= 400
[Simplify.]

f(x) = 4002
[Speed for 2 hours.]

= 200
[Simplify.]

f(x) = 4003
[Speed for 3 hours.]

= 133.33
[Simplify.]

f(x) = 4004
[Speed for 4 hours.]

= 100
[Simplify.]

Graph 1 represents the function.

5.
Which of the graphs represents the exponential function $f$($x$) = 2 × 4$x$, for $x$ = - 2, - 1, 0, 1, 2?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 2 x 4x
[Original equation.]

f(-2) = 2 x 4-2
[Replace -2 for x.]

= 0.125
[Simplify.]

f(-1) = 2 x 4-1
[Replace -1 for x.]

= 0.5
[Simplify.]

f(0) = 2 x 40
[Replace 0 for x.]

= 2
[Simplify.]

f(1) = 2 x 41
[Replace 1 for x.]

= 8
[Simplify.]

f(2) = 2 x 42
[Replace 2 for x.]

= 32
[Simplify.]

Graph 1 represents the function for x = - 2, - 1, 0,1,2.

6.
Find the value of output $f$($x$), for $x$ = -1, 0, 1, 2, 3, if $f$($x$) =3$x$ - 4.
 a. $f$(-1, 0, 1, 2, 3) = (-2.67, -3, -1, 4, 23) b. $f$(-1, 0, 1, 2, 3) = (-3.67, -3, -1, 5, 23) c. $f$(-1, 0, 1, 2, 3) = (23, -3, -1, 5, -3.67) d. $f$(-1, 0, 1, 2, 3) = (-3, -3.67, -2, 5, 23)

#### Solution:

f(x) = 3x - 4
[Given function.]

f(-1) = 3-1 - 4
[Substitute -1 for x.]

= -3.67
[Simplify.]

f(0) = 30 - 4
[Substitute 0 for x.]

= -3
[Simplify.]

f(1) = 31 - 4
[Substitute 1 for x.]

= -1
[Simplify.]

f(2) = 32 - 4
[Substitute 2 for x.]

= 5
[Simplify.]

f(3) = 33 - 4
[Substitute 3 for x.]

= 23
[Simplify.]

The output values of f(x), for x = -1, 0, 1,2,3, if f(x) = 3x - 4 are -3.67, -3, -1, 5, 23 respectively.

7.
Cresida borrowed $200 from her friend to purchase a Xerox machine at 10% compound interest. The function $f$ ($x$) = 200(1.10)$x$ describes the money she has to pay after $x$ years. Which of the graphs represents the function over a period of 4 years?  a. Graph 1 b. Graph 2 #### Solution: f(x) = 200(1.10)x [Given function.] f(0) = 200(1.10)0 [Substitute 0 for x.] = 200 [Simplify.] f(1) = 200(1.10)1 [Substitute 1 for x.] = 220 [Simplify.] f(2) = 200(1.10)2 [Substitute 2 for x.] = 242 [Simplify.] f(3) = 200(1.10)3 [Substitute 3 for x.] = 266.2 [Simplify.] f(4) = 200(1.10)4 [Substitute 4 for x.] = 292.82 [Simplify.] The money Cresida has to pay after 4 years is$292.82.

Among the graphs, Graph 1 represents the function over a period of 4 years.

8.
Which of the graphs represents the function $f$($x$) = $x$2 for the values of $x$ = 0, 1, 2 and 3?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = x2
[Original equation.]

f(0) = (0)2
[Substitute 0 for x.]

= 0
[Simplify.]

f(1) = (1)2
[Substitute 1 for x.]

= 1
[Simplify.]

f(2) = (2)2
[Substitute 2 for x.]

= 4
[Simplify.]

f(3) = (3)2
[Substitute 3 for x.]

= 9
[Simplify.]

Graph 1 satisfies the equation f(x) = x2 .

9.
Which of the graphs represents the function $f$($x$) = 10$x$2 + 50 for the values of $x$ = 0, 1, 2 and 3.

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 10x2 + 50
[Original equation.]

f(0) = 10 x (0)2 + 50
[Substitute x = 0.]

= 50
[Simplify.]

f(1) = 10 x (1)2 + 50
[Substitute x = 1.]

= 60
[Simplify.]

f(2) = 10 x (2)2 + 50
[Substitute x = 2.]

= 90
[Simplify.]

f(3) = 10 x (3)2 + 50
[Substitute x = 3.]

= 140
[Simplify.]

Graph 2 represents the function f(x) = 10x2 + 50.

10.
Which of the graphs represents the function $f$($x$) = 2$x$2 - 2?

 a. Graph 1 b. Graph 2

#### Solution:

f(x) = 2x2 - 2
[Original equation.]

f(-1) = 2 × (-1)2 - 2
[Substitute x = -1.]

= 0
[Simplify.]

f(0) = 2 × (0)2 - 2
[Substitute x = 0.]

= -2
[Simplify.]

f(1) = 2 × (1)2 - 2
[Substitute x = 1.]

= 0
[Simplify.]

f(2) = 2 × (2)2 - 2
[Substitute x = 2.]

= 6
[Simplify.]

f(3) = 2 × (3)2 - 2
[Substitute x = 3.]

= 16
[Simplify.]

Graph 2 represents the function f(x) = 2x2 - 2.