Question 1

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$ (x - 2)^2$ + (y + 3)^2$ = 25 $$

Question 2

A company’s profit $$P (in $$thousands of dollars) after $$x$$ months is modeled by $$P(x) = -2x^2$ + 12x + 20. $$What is the maximum profit, and after how many months does it occur?

Accepted Answer

$$ 38 $$ thousand dollars after $$3$$ months

Question 3

Which of the following is the correct solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$ -1 \u003c x \u003c 6 $$

Question 4

Given $$f(x) = \sqrt{x-1}$$ and $$g(x) = x^2$ + 1$$, what is the domain of the composite function $$f(g(x))$$?

Accepted Answer

$$ (-\infty, \infty) $$

Question 5

Which of the following statements is TRUE about the function $$f(x) = x^3$?

Accepted Answer

$$ f(x)  is an $$odd function and its graph is symmetric with respect to the origin.

Question 6

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$ x = 2, y = 1 $$

Question 7

Which of the following is the inverse of the function $$f(x) = 3x - 4$$?

Accepted Answer

$$ f$$^{-1}$$(x) = \frac{x + 4}{3} $$

Question 8

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20$ years? (Round to the nearest whole number.)

Accepted Answer

$$ 37 $$ units

Question 9

Which of the following is equivalent to $$\log_2$(8x)$$?

Accepted Answer

$$ 3 + \log_2$(x) $$

Question 10

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$ (x + 2)^2$ - 4 $$

Question 11

Which of the following is the correct solution to $$2^{x} = 10$?

Accepted Answer

$$ x = \log_2$(10) $$

Question 12

A rational function has a vertical asymptote at $$x = 3$$ and a hole at $$x = -2. $$Which of the following could be its equation?

Accepted Answer

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

Question 13

Which of the following is the simplified form of $$\frac{3 + 4i}{1 - 2i}$$?

Accepted Answer

$$ -1 + 2i $$

Question 14

Which of the following best describes the graph of $$y = |x - 2| + 3$$ compared to $$y = |x|$$?

Accepted Answer

$$ y = |x - 2| + 3  is $$shifted $$2$$ units right and $$3$$ units up.

Question 15

Which of the following is the correct solution set for the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$ 2 \u003c x \u003c 3 $$

Question 16

Given the function $$f(x) = \frac{1}{x - 4}$$, what is the domain?

Accepted Answer

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

Question 17

If $$i is $$the imaginary unit, what is $$i^{23}$$?

Accepted Answer

$$ -i $$

Question 18

A population of bacteria triples every $$4$$ hours. If the initial population is $$200$$, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$ P = 200 \cdot 3$$^{t/4}$$ $$

Question 19

Which of the following relations is NOT a function?

Accepted Answer

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

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