Q: Which of the following best 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 is the correct definition of a polynomial function?

Accepted Answer

A function that can be written as $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, where $a_i$ are real numbers and $n$ is a non-negative integer.

Question 2

Which of the following is the domain of the function $f(x) = \sqrt{x-3}$?

Accepted Answer

$x \geq 3$

Question 3

A company models its profit $P$ (in thousands of dollars) as $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $18$ thousand dollars at $x = 2$ thousand units.

Question 4

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 5

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

Accepted Answer

$x = 2,\ y = 1$

Question 6

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

Accepted Answer

$-1 < x < 6$

Question 7

A population of bacteria triples every 4 hours. If the initial population is 200, what will the population be after 12 hours?

Accepted Answer

$5400$

Question 8

Which of the following is the inverse function of $f(x) = 3x - 7$?

Accepted Answer

$f^{-1}(x) = \frac{x+7}{3}$

Question 9

If $f(x) = x^2 - 4x + 3$ and $g(x) = 2x - 1$, what is $(f \circ g)(x)$?

Accepted Answer

$4x^2 - 20x + 24$

Question 10

Which of the following is the solution to the equation $\log_2(x) = 5$?

Accepted Answer

$x = 32$

Question 11

A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots. Which of the following must be true?

Accepted Answer

$b^2 - 4ac = 0$

Question 12

A car depreciates in value by 15% each year. If the car is currently worth $\$20,000$, what will its value be after 3 years?

Accepted Answer

$\$12,282.50$

Question 13

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

Accepted Answer

$x = 3$

Question 14

Given the function $f(x) = \frac{2x+1}{x-3}$, what is the vertical asymptote?

Accepted Answer

$x = 3$

Question 15

A student invests $\$1000$ in an account that pays 6% annual interest compounded quarterly. What will the balance be after 2 years? (Round to the nearest dollar)

Accepted Answer

$\$1127$

Question 16

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

Accepted Answer

$x = 2,\ x = 3$

Question 17

Which of the following best 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 18

A patient is given a dose of medication that decays exponentially in the body according to $A(t) = 50e^{-0.2t}$, where $A$ is the amount in mg and $t$ is time in hours. How much medication remains after 5 hours? (Round to the nearest mg)

Accepted Answer

$18$ mg

Question 19

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

Accepted Answer

$x = 24$

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