Power Functions with Modeling Worksheet

**Page 1**

1.

If $f$($x$) = $x$^{$n$} , $n$ is a positive integer is an odd function, then which of the following is correct for the function $g$($x$) = $x$^{$n$+3} .

a. | $g$($x$) is an even function | ||

b. | $g$($x$) is neither even nor odd | ||

c. | $g$($x$) is an odd function | ||

d. | None of the above |

So,

[Definition of an odd function.]

(-

(- 1)

[Divide both sides by

(- 1)

[

So,

= 4, or 6, or 8, . . . and hence

[Replace

= (- 1)

=

[

So,

Correct answer : (1)

2.

Write the domain of the function $f$($x$) = 9 $\sqrt{x}$.

a. | (- ∞ , 0] | ||

b. | (0, ∞) | ||

c. | ( - ∞ , 0) | ||

d. | [0, ∞) |

Correct answer : (4)

3.

Find the constant of variation for the function $f$ ($x$) = 6($\sqrt[11]{x}$).

a. | 6 | ||

b. | $\frac{1}{11}$ | ||

c. | 11 |

= 6 ·

On comparing

The constant of variation of the given function is

[The constant of variation of

Correct answer : (1)

4.

Find the value of $f$(32), if $f$($x$) = 28 ${x}^{\frac{-1}{5}}$.

a. | 28 | ||

b. | 19 | ||

c. | 42 | ||

d. | 14 |

[Substitute

= 28

[Use 2

(28) (2)

[Use

= (28)(

[Use

Correct answer : (4)

5.

Find the power for the function $g$($x$) = $\frac{9}{{x}^{4}}$.

a. | 4 | ||

b. | - 4 | ||

c. | 9 |

= 9 ·

= 9 ·

On comparing

The power of the given function is

[The power of the function

Correct answer : (2)

6.

Let $f$($x$) = 8$x$^{- 17} . Which of the following is correct?

a. | $f$ is a constance function | ||

b. | $f$ is neither an even nor an odd function | ||

c. | $f$ is an even function | ||

d. | $f$ is an odd function |

So,

Correct answer : (4)

7.

Let $f$($x$) = 2$x$^{12}. Which of the following is correct?

a. | $f$($x$) is a constant function | ||

b. | $f$($x$) is an odd function | ||

c. | $f$($x$) is neither an odd function nor an even function | ||

d. | $f$($x$) is an even function |

So,

Correct answer : (4)

8.

Choose the monomial function from the following.

a. | $y$ = 3$x$ ^{- 5} | ||

b. | $y$ = 6${x}^{\frac{1}{5}}$ | ||

c. | $y$ = 5$x$ ^{4} | ||

d. | $y$ = ${x}^{\frac{-1}{5}}$ |

[Definition of monomial function.]

Clearly, from the given choices,

Correct answer : (3)

9.

Let $f$($x$) = 3$x$^{3} , which of the following is correct?

a. | $f$($x$) is an function | ||

b. | The graph of $f$($x$) is symmetric with respect to $x$ - axis | ||

c. | The graph of $f$($x$) is symmetric with respect to the origin | ||

d. | The graph of $f$($x$) symmetric with respect to $y$ - axis |

Since

Correct answer : (3)

10.

Let $f$($x$) = - $x$^{0.8} . Which of the following is correct?

a. | The graph of $f$($x$) is symmetric with respect to the $x$ - axis | ||

b. | The graph of $f$($x$) is symmetric with respect to the $y$ - axis | ||

c. | $f$($x$) is an odd function | ||

d. | The graph of $f$($x$) is symmetric with respect to the origin |

= - (

[Use

= - (-

= - (

So,

Correct answer : (2)