Q: Which of the following describes the end behavior of the polynomial $f(x) = -2x^4 + 5x^2 - 3$?

As $x \to \infty$, $f(x) \to -\infty$; as $x \to -\infty$, $f(x) \to -\infty$

Question 1

Which of the following best describes the solution set of the equation $x^2 - 5x + 6 = 0$?

Accepted Answer

$x = 2$ and $x = 3$

Question 2

A company models its profit $P$ (in thousands of dollars) as a function of the number of units sold $x$ by $P(x) = -2x^2 + 40x - 100$. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $300$ at $x = 10$

Question 3

Which of the following is the correct factorization of $x^3 - 8$?

Accepted Answer

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

Question 4

If $f(x) = 3x - 7$ and $g(x) = x^2$, what is $(f \circ g)(2)$?

Accepted Answer

$5$

Question 5

A population of bacteria triples every 4 hours. If the initial population is 500, which equation models the population $P$ after $t$ hours?

Accepted Answer

$P = 500 \cdot 3^{t/4}$

Question 6

Solve for $x$: $\log_2(x) + \log_2(x-2) = 3$.

Accepted Answer

$x = 4$

Question 7

Which of the following describes the end behavior of the polynomial $f(x) = -2x^4 + 5x^2 - 3$?

Accepted Answer

As $x 	o \infty$, $f(x) 	o -\infty$; as $x 	o -\infty$, $f(x) 	o -\infty$

Question 8

A ball is thrown upward from a height of 2 meters with an initial velocity of 20 m/s. Its height after $t$ seconds is given by $h(t) = -4.9t^2 + 20t + 2$. After how many seconds does the ball reach its maximum height?

Accepted Answer

$t = 2.04$ seconds

Question 9

Which of the following is the inverse function of $f(x) = \frac{2x - 5}{3}$?

Accepted Answer

$f^{-1}(x) = \frac{3x + 5}{2}$

Question 10

Given the system of equations: $\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$, what is the solution $(x, y)$?

Accepted Answer

$(2, 1)$

Question 11

Which of the following is the correct domain of the function $f(x) = \frac{1}{x^2 - 9}$?

Accepted Answer

$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$

Question 12

A radioactive substance decays according to $A(t) = 100e^{-0.2t}$, where $A$ is the amount remaining after $t$ years. How much remains after 5 years (rounded to the nearest whole number)?

Accepted Answer

$37$

Question 13

Which of the following is the solution to the inequality $|2x - 3| < 5$?

Accepted Answer

$-1 < x < 4$

Question 14

If $f(x) = x^2 - 4x + 7$, what is the vertex of the parabola?

Accepted Answer

$(2, 3)$

Question 15

A car rental company charges a flat fee of $\$30$ plus $\$0.20$ per mile driven. Which equation models the total cost $C$ for driving $x$ miles?

Accepted Answer

$C = 0.20x + 30$

Question 16

Which of the following is the solution to $\sqrt{x + 5} = x - 1$?

Accepted Answer

$x = 2$

Question 17

A quadratic function models the height $h$ (in meters) of a diver above water as $h(t) = -5t^2 + 10t + 3$. How long is the diver above 8 meters?

Accepted Answer

$0 < t < 2$

Question 18

Which of the following is the correct solution to $2^{x+1} = 16$?

Accepted Answer

$x = 3$

Question 19

If $f(x) = \sqrt{x - 1}$, what is the domain of $f$?

Accepted Answer

$[1, \infty)$

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