Question 1

Which of the following is a correct example of a power function?

Accepted Answer

$$f(x) = 3x^2$

Question 2

The area $$A of a $$circle with radius $$r is $$given by $$A = \pi r^2$. Which statement best describes the relationship between A$ and r$?

Accepted Answer

$$A$$ varies directly as the square of $$r$$

Question 3

Which of the following formulas represents a rational function that is also a power function?

Accepted Answer

$$V = \dfrac{k}{P}$$

Question 4

Boyle's Law states that the volume $$V of a $$gas at constant temperature is inversely proportional to the pressure $$P. $$Which equation expresses this relationship?

Accepted Answer

$$V = \dfrac{k}{P}$$

Question 5

If the circumference $$C of a $$circle is given by $$C = 2\pi r$$, what is the constant of variation?

Accepted Answer

$$2\pi$$

Question 6

Which of the following best describes the function $$f(x) = kx^n$$ where $$k 
eq 0$$ and $$n is a $$real number?

Accepted Answer

A power function

Question 7

A scientist finds that the force $$F$$ between two objects is inversely proportional to the square of the distance $$d$$ between them. Which equation models this relationship?

Accepted Answer

$$F = \dfrac{k}{d^2$}$$

Question 8

Which of the following is NOT a power function?

Accepted Answer

$$f(x) = 2^x$$

Question 9

If $$y$$ varies directly as $$x^3$$, and $$y = 24$$ when $$x = 2$$, what is the value of $$y$$ when $$x = 3$$?

Accepted Answer

$$y = 81$$

Question 10

Which of the following real-world scenarios is best modeled by a power function?

Accepted Answer

The area of a square as a function of its side length

Question 11

Given the function $$f(x) = 4x$$^{-2}$$, which of the following statements is true?

Accepted Answer

It is a power function with a negative exponent

Question 12

If the area $$A of a $$circle is quadrupled, by what factor does the radius $$r$$ increase?

Accepted Answer

$$2$$

Question 13

Which of the following best describes the relationship between the volume $$V$$ and pressure $$P in $$Boyle's Law?

Accepted Answer

$$V is $$inversely proportional to $$P$$

Question 14

A function $$f(x) is $$defined as $$f(x) = 7x$$^{1/2}$$. Which of the following is true?

Accepted Answer

It is a power function with exponent $$1/2$$

Question 15

If the force of gravity $$F$$ acting on an object is inversely proportional to the square of the distance $$d$$ from the center of the Earth, what happens to $$F if$$ $$d is $$doubled?

Accepted Answer

$$F$$ becomes one-fourth its original value

Question 16

Which of the following statements is true about the function $$f(x) = kx^n$$?

Accepted Answer

If $$n \u003c 0$$, $$f(x) is a $$rational function

Question 17

A car's stopping distance $$d is $$proportional to the square of its speed $$v. If $$the speed is tripled, by what factor does the stopping distance increase?

Accepted Answer

$$9$$

Question 18

Which of the following is the general form of a linear function?

Accepted Answer

$$f(x) = kx + b$$

Question 19

If $$y$$ varies inversely as $$x$$, and $$y = 10$$ when $$x = 2$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 4$$

Question 20

Which of the following best describes the relationship between the circumference $$C$$ and the radius $$r of a $$circle?

Accepted Answer

$$C is $$directly proportional to $$r$$

Power Functions and Variation: Definitions, Properties, and Applications

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