Q: A medical researcher is tracking the spread of a virus. The number of cases $C$ is modeled by $C(t) = 5t + 9$, where $t$ is the number of days since the outbreak. What is the inverse function, and what does it represent?

$C^{-1}(x) = \frac{x-9}{5}$; it gives the number of days since the outbreak for a given number of cases.

Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$\{(1,2), (3,4), (5,5)\}$

Question 2

Given the points $(-1,3)$ and $(3,4)$, what is the slope of the line passing through them, and does the line rise, fall, is horizontal, or vertical?

Accepted Answer

Slope is $\frac{1}{4}$; the line rises.

Question 3

Given the equation of a line passing through $(3,5)$ with a slope of $2$, what is the equation in point-slope form?

Accepted Answer

$y - 5 = 2(x - 3)$

Question 4

A line passes through $(2, -3)$ and is perpendicular to the line $y = \frac{1}{5}x + 6$. What is the slope of the required line?

Accepted Answer

$-5$

Question 5

Given $f(x) = x^3$, which of the following describes the domain and range of $f$?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $(-\infty, \infty)$

Question 6

What is the distance between the points $(-2, -6)$ and $(3, -4)$?

Accepted Answer

$\sqrt{29}$

Question 7

Find the midpoint of the segment with endpoints $(10, 4)$ and $(2, 6)$.

Accepted Answer

$(6, 5)$

Question 8

Which of the following is the correct inverse of $f(x) = 2x + 3$?

Accepted Answer

$f^{-1}(x) = \frac{x-3}{2}$

Question 9

Given the circle $(x-4)^2 + (y-1)^2 = 16$, what is the center and radius?

Accepted Answer

Center: $(4,1)$, Radius: $4$

Question 10

What is the domain of $f(x) = \frac{3}{x-4}$?

Accepted Answer

$(-\infty, 4) \cup (4, \infty)$

Question 11

Which transformation is applied to $f(x) = |x|$ to obtain $g(x) = -2(|x+2|^2) + 1$?

Accepted Answer

Shift left 2, vertical stretch by 2, reflect over x-axis, square, shift up 1

Question 12

Given $f(x) = 3x + 8$ and $g(x) = \frac{x-8}{3}$, are $f$ and $g$ inverses of each other?

Accepted Answer

Yes, because $f(g(x)) = x$ and $g(f(x)) = x$

Question 13

Evaluate $f(-3)$ for $f(x) = \begin{cases} x-1 & x < 0 \ 7x+3 & x \geq 0 \end{cases}$

Accepted Answer

$-4$

Question 14

A medical researcher is tracking the spread of a virus. The number of cases $C$ is modeled by $C(t) = 5t + 9$, where $t$ is the number of days since the outbreak. What is the inverse function, and what does it represent?

Accepted Answer

$C^{-1}(x) = \frac{x-9}{5}$; it gives the number of days since the outbreak for a given number of cases.

Question 15

Which of the following best describes the range of the function $f(x) = \sqrt{24 - 3x}$?

Accepted Answer

$[0, \sqrt{24}]$

Question 16

A city plans to build a circular park with equation $(x-5)^2 + (y+2)^2 = 49$. What is the center and radius of the park?

Accepted Answer

Center: $(5, -2)$, Radius: $7$

Question 17

Given the function $g(x) = \begin{cases} x+3 & x \geq -3 \ -(x+3) & x < -3 \end{cases}$, what is $g(-6)$?

Accepted Answer

$3$

Question 18

A biologist measures the distance between two points on a petri dish: $(4,1)$ and $(6,3)$. What is the distance?

Accepted Answer

$2\sqrt{2}$

Question 19

Which of the following is the correct midpoint of the segment with endpoints $(-4,7)$ and $(1,-3)$?

Accepted Answer

$\left(-\frac{3}{2}, 2\right)$

Question 20

Given $f(x) = 5x - 9$ and $g(x) = \frac{x+5}{9}$, are $f$ and $g$ inverses of each other?

Accepted Answer

No, because $f(g(x)) 
eq x$

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