Q: Given $f(x) = x^4 - 2x^2 + 1$, which of the following describes the end behavior of $f(x)$?

As $x \to \pm\infty$, $f(x) \to \infty$

Question 1

Given the function $f(x) = x^3 - 6x^2 + 9x$, which of the following intervals is where the function is decreasing?

Accepted Answer

$(0, 3)$

Question 2

Suppose the graph of $f(x)$ is reflected over the $y$-axis and shifted up 2 units. Which equation represents the new function?

Accepted Answer

$f(-x) + 2$

Question 3

Find the domain of the function $f(x) = \dfrac{2x}{x^2 - 9}$.

Accepted Answer

$x 
eq \pm 3$

Question 4

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 distance $d$ (in feet) of the ball from the ground after $t$ seconds is given by $d(t) = -16t^2 + 80t + 800$. What is the maximum height of the ball?

Accepted Answer

$1000$ feet

Question 5

Given $f(x) = x^4 - 2x^2 + 1$, which of the following describes the end behavior of $f(x)$?

Accepted Answer

As $x 	o \pm\infty$, $f(x) 	o \infty$

Question 6

Which of the following is the sum of $f(x) = x^2 - 9x$ and $g(x) = 2x + 3$?

Accepted Answer

$x^2 - 7x + 3$

Question 7

A radioactive substance decays according to the model $A(t) = Ae^{-0.07t}$, where $A$ is the initial amount present and $t$ is time in years. After 12 years, what percent of the original amount remains?

Accepted Answer

$43\%$

Question 8

Which of the following functions is odd?

Accepted Answer

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

Question 9

Given $f(x) = x^2 - 4x + 3$, find the $x$-intercepts of the function.

Accepted Answer

$x = 1$ and $x = 3$

Question 10

Which of the following is the correct expression for $\log(x^2 - 9) - \log(x - 3)$ as a single logarithm?

Accepted Answer

$\log\left(\dfrac{x^2 - 9}{x - 3}\right)$

Question 11

A company charges a fixed cost of $1500$ with a variable cost per unit of $22$. The commodity is sold for $50$ per unit. Which equation models the profit $P$ for $x$ units sold?

Accepted Answer

$P = 50x - 22x - 1500$

Question 12

Find the solution to the system of equations: $\begin{cases} 2x + 3y = 12 \ x - y = 2 \end{cases}$

Accepted Answer

$x = 4, y = 2$

Question 13

Suppose $f(x) = \sqrt{x - 2}$. What is the domain of $f(x)$?

Accepted Answer

$x \geq 2$

Question 14

Which of the following is the correct solution to $4^x = 64$?

Accepted Answer

$x = 3$

Question 15

Given $f(x) = x^2$ and $g(x) = 2x + 3$, which of the following is $f(g(x))$?

Accepted Answer

$(2x + 3)^2$

Question 16

A large group of students is asked to memorize a list of 60 Italian words. The number of words retained is modeled by $W(t) = 60e^{-0.2t}$, where $t$ is the number of hours after memorization. How many words are remembered after 5 hours?

Accepted Answer

$22$

Question 17

Which of the following is the correct expression for the difference quotient of $f(x) = x^2$?

Accepted Answer

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

Question 18

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

Accepted Answer

$x = \ln(1.5)$

Question 19

Given $f(x) = x^2 - 4$, which of the following is the inverse function $f^{-1}(x)$?

Accepted Answer

$f^{-1}(x) = \sqrt{x + 4}$ and $f^{-1}(x) = -\sqrt{x + 4}$

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