Nonlinear Function Worksheet

**Page 1**

1.

Which of the graphs represents the function $f$($x$) = $\frac{6}{\mathrm{x}}$, for $x$ = 1, 2, 3, 4?

a. | Graph 1 | ||

b. | Graph 2 |

[Original equation.]

[Substitute 1 for

= 6

[Simplify.]

[Substitute 2 for

= 3

[Simplify.]

[Substitute 3 for

= 2

[Simplify.]

[Substitute 4 for

= 1.5

[Simplify.]

Graph 2 satisfies the solution.

Correct answer : (2)

2.

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

a. | Graph 1 | ||

b. | Graph 2 |

[Original equation.]

[Substitute the value of

[Substitute the value of

[Substitute the value of

[Substitute the value of

[Substitute the value of

[Substitute the value of

Graph 1 represents the function

Correct answer : (1)

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 |

[Original equation.]

[Substitute 0 for

= 0

[Simplify.]

[Substitute 1 for

= 2

[Simplify.]

[Substitute 2 for

= 8

[Simplify.]

[Substitute 3 for

= 18

[Simplify.]

Graph 2 satisfies the equation.

Correct answer : (2)

4.

Mike left his home and drove to his parents' house, which is 400 miles away. The function $f$($x$) = $\frac{400}{\mathrm{x}}$ 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 |

[Original equation.]

[Speed for 1 hour.]

= 400

[Simplify.]

[Speed for 2 hours.]

= 200

[Simplify.]

[Speed for 3 hours.]

= 133.33

[Simplify.]

[Speed for 4 hours.]

= 100

[Simplify.]

Graph 1 represents the function.

Correct answer : (1)

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 |

[Original equation.]

[Replace -2 for

= 0.125

[Simplify.]

[Replace -1 for

= 0.5

[Simplify.]

[Replace 0 for

= 2

[Simplify.]

[Replace 1 for

= 8

[Simplify.]

[Replace 2 for

= 32

[Simplify.]

Graph 1 represents the function for

Correct answer : (1)

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) |

[Given function.]

[Substitute -1 for

= -3.67

[Simplify.]

[Substitute 0 for

= -3

[Simplify.]

[Substitute 1 for

= -1

[Simplify.]

[Substitute 2 for

= 5

[Simplify.]

[Substitute 3 for

= 23

[Simplify.]

The output values of

Correct answer : (2)

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 |

[Given function.]

[Substitute 0 for

= 200

[Simplify.]

[Substitute 1 for

= 220

[Simplify.]

[Substitute 2 for

= 242

[Simplify.]

[Substitute 3 for

= 266.2

[Simplify.]

[Substitute 4 for

= 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.

Correct answer : (1)

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 |

[Original equation.]

[Substitute 0 for

= 0

[Simplify.]

[Substitute 1 for

= 1

[Simplify.]

[Substitute 2 for

= 4

[Simplify.]

[Substitute 3 for

= 9

[Simplify.]

Graph 1 satisfies the equation

Correct answer : (1)

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 |

[Original equation.]

[Substitute

= 50

[Simplify.]

[Substitute

= 60

[Simplify.]

[Substitute

= 90

[Simplify.]

[Substitute

= 140

[Simplify.]

Graph 2 represents the function

Correct answer : (2)

10.

Which of the graphs represents the function $f$($x$) = 2$x$^{2} - 2?

a. | Graph 1 | ||

b. | Graph 2 |

[Original equation.]

[Substitute

= 0

[Simplify.]

[Substitute

= -2

[Simplify.]

[Substitute

= 0

[Simplify.]

[Substitute

= 6

[Simplify.]

[Substitute

= 16

[Simplify.]

Graph 2 represents the function

Correct answer : (2)