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

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