Q: Given the function $f(x) = x^3 - 2x^2 + x - 5$, which of the following is the correct end behavior of the graph?

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

Q: Which of the following is the correct domain for the function $f(x) = \dfrac{1}{x^2 - 4}$?

$x \in \mathbb{R}, x \neq -2, 2$

Question 1

Given the function $f(x) = x^3 - 2x^2 + x - 5$, which of the following is the correct end behavior of the graph?

Accepted Answer

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

Question 2

A ball is thrown vertically upward from the top of a building 800 feet tall with an initial velocity of 80 feet per second. The height $h$ (in feet) of the ball after $t$ seconds is given by $h(t) = -16t^2 + 80t + 800$. What is the maximum height of the ball?

Accepted Answer

$1000$ feet

Question 3

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3 - 2x$

Question 4

Suppose a company’s profit function is $P(x) = 52x - 1500$, where $x$ is the number of units sold. What is the break-even point?

Accepted Answer

$x = 28.85$

Question 5

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

Accepted Answer

$(2x + 3)^2 - 4$

Question 6

A radioactive substance decays according to the model $A(t) = Ae^{-kt}$, where $A$ is the initial amount and $k$ is a positive constant. If after 47.3 years, 80% of the original amount remains, what is the approximate half-life?

Accepted Answer

$106$ years

Question 7

Which of the following is the correct domain for the function $f(x) = \dfrac{1}{x^2 - 4}$?

Accepted Answer

$x \in \mathbb{R}, x 
eq -2, 2$

Question 8

If the polynomial $f(x) = x^4 - 2x^3 + x^2 - 2x + 1$ is divided by $x - 1$, what is the remainder?

Accepted Answer

$1$

Question 9

Which of the following equations represents a horizontal asymptote for the function $f(x) = \dfrac{3x^2 + 2x + 1}{x^2 - 4}$?

Accepted Answer

$y = 3$

Question 10

A large group of students is asked to memorize a list of 60 Italian words. Suppose that the number of words remembered after $t$ hours is modeled by the function $W(t) = 60(1 - e^{-0.5t})$. What is the horizontal asymptote of the graph of this function and what does it represent?

Accepted Answer

$y = 60$, representing the maximum number of words remembered

Question 11

Which of the following is the correct solution to $\log_2(x) + \log_2(x - 1) = \log_2(6)$?

Accepted Answer

$x = 3$

Question 12

Given the system of equations: $\begin{cases} 2x - 4y = -12 \ x + 2y = 4 \end{cases}$, what is the solution using Gauss-Jordan elimination?

Accepted Answer

$(1, -3)$

Question 13

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

Accepted Answer

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

Question 14

If $f(x) = x^2 - 4x + 3$, what are the zeros and their multiplicities?

Accepted Answer

Zeros: $x = 1$ (multiplicity 1), $x = 3$ (multiplicity 1)

Question 15

Which of the following is the correct solution to $6e^x = 9$?

Accepted Answer

$x = \ln(1.5)$

Question 16

A company charges a fixed cost of $1500 with a variable cost per unit of $22$. The revenue function is $R(x) = 52x$. What is the profit function?

Accepted Answer

$P(x) = 52x - 22x - 1500$

Question 17

Which of the following is the correct solution to $x^2 = 128$?

Accepted Answer

$x = \pm 8\sqrt{2}$

Question 18

Given the function $f(x) = \dfrac{2x}{x^2 - 4}$, which of the following is the correct vertical asymptote?

Accepted Answer

$x = -2$ and $x = 2$

Question 19

Which of the following is the correct solution to $\log_3(x) = 4$?

Accepted Answer

$x = 81$

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