Question 1

Given the function $$f(x) = \frac{x-3}{x+2}$$, which of the following statements is TRUE about its asymptotes?

Accepted Answer

The function has a vertical asymptote at $$x = -2$$ and a horizontal asymptote at $$y = 1.$$

Question 2

Which of the following equations represents a direct variation between $$y$$ and $$x$$?

Accepted Answer

$$y = 5x$$

Question 3

If $$y$$ varies inversely with $$x$$ and $$y = 4$$ when $$x = 3$$, what is $$y$$ when $$x = 6$$?

Accepted Answer

$$y = 2$$

Question 4

A car rental company charges a base fee of $$400 plus 200 $$per credit hour. Which equation best models the total cost $$C as a $$function of the number of credit hours $$h$$?

Accepted Answer

$$C = 400 + 200h$$

Question 5

The circumference $$C of a $$circle varies directly with its radius $$r. If$$ $$C = 31.4$$ when $$r = 5$$, what is the value of the constant of variation $$k$$?

Accepted Answer

$$k = 6.28$$

Question 6

The volume $$V of $$blood in a human body varies directly as the weight $$W of $$the body. If a person weighing $$160$$ pounds has $$5$$ quarts of blood, how many quarts of blood does a person weighing $$220$$ pounds have?

Accepted Answer

$$6.875$$ quarts

Question 7

Which of the following graphs could represent a direct variation between $$y$$ and $$x$$?

Accepted Answer

A straight line passing through the origin

Question 8

If $$y$$ varies jointly as $$x$$ and $$z$$, and $$y = 24$$ when $$x = 2$$ and $$z = 3$$, what is the value of the constant of variation $$k$$?

Accepted Answer

$$k = 4$$

Question 9

Boyle's Law states that the pressure $$P of a $$gas varies inversely with its volume $$V. If$$ $$P = 200$$ psi when $$V = 35$$ cubic inches, what is the pressure when the volume is increased to $$50$$ cubic inches?

Accepted Answer

$$P = 140$$ psi

Question 10

The intensity $$I of $$sound varies inversely with the square of the distance $$d$$ from the source. If $$I = 100$$ units when $$d = 2$$ meters, what is $$I$$ when $$d = 5$$ meters?

Accepted Answer

$$I = 16$$ units

Question 11

Which of the following is the correct variation equation for the statement: 'The time $$T to $$travel a fixed distance varies inversely with the speed $$v$$'?

Accepted Answer

$$T = \frac{k}{v}$$

Question 12

If $$y$$ varies directly as $$x^2$$ and $$y = 18$$ when $$x = 3$$, what is $$y$$ when $$x = 5$$?

Accepted Answer

$$y = 50$$

Question 13

The resistance $$R of a $$copper wire varies directly with its length $$l$$ and inversely with the square of its diameter $$d. $$Which equation best models this relationship?

Accepted Answer

$$R = k \frac{l}{d^2$}$$

Question 14

If $$y$$ varies inversely as $$x$$ and $$y = 10$$ when $$x = 4$$, what is the constant of variation $$k$$?

Accepted Answer

$$k = 40$$

Question 15

A person's BMI varies jointly as their weight $$W$$ and inversely as the square of their height $$h. If a $$person weighs $$170$$ pounds and is $$5.5$$ feet tall with a BMI of $$28.5$$, what is the constant of variation $$k$$?

Accepted Answer

$$k = 20.3$$

Question 16

Which of the following is NOT a characteristic of a rational function of the form $$f(x) = \frac{ax + b}{cx + d}$$?

Accepted Answer

It always passes through the origin.

Question 17

If $$y$$ varies directly as $$x$$ and $$y = 15$$ when $$x = 3$$, what is $$y$$ when $$x = 7$$?

Accepted Answer

$$y = 35$$

Question 18

Which of the following best describes joint variation?

Accepted Answer

A variable varies directly as the product of two or more other variables.

Question 19

If $$y$$ varies inversely as $$x^2$$ and $$y = 8$$ when $$x = 2$$, what is $$y$$ when $$x = 4$$?

Accepted Answer

$$y = 2$$

E7

Guida di studio - Domande di pratica

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