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

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

Question 1

Solve the linear equation: $-2(3x + 4) - 2x = 5(x - 2) - 4$

Accepted Answer

$x = -4$

Question 2

Which of the following is the domain of the function $f(x) = \dfrac{x-1}{x^2-3}$?

Accepted Answer

$(-\infty, -\sqrt{3}) \cup (-\sqrt{3}, \sqrt{3}) \cup (\sqrt{3}, \infty)$

Question 3

A manufacturer has a monthly fixed cost of $150,000$ and a production cost of $18$ for each unit produced. The product sells for $24$ per unit. Let $x$ represent the number of units sold. Which function represents the total cost?

Accepted Answer

$C(x) = 150,000 + 18x$

Question 4

Solve the quadratic equation: $x^2 - 10x = 3$

Accepted Answer

$x = 5 \pm \sqrt{28}$

Question 5

Which of the following best describes the end behavior of the function $f(x) = -x^3 + 3x^2 - 2x + 3$?

Accepted Answer

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

Question 6

A farmer has $1000$ ft of fence to enclose a rectangular area. If there is a barn on one side, so no fencing is required there, what is the maximum area that can be enclosed?

Accepted Answer

$250,000$ sq ft

Question 7

Solve the inequality: $2(2x - 1) > 4(x + 2) - 4x$

Accepted Answer

$x > 2$

Question 8

Which of the following is the inverse of the function $f(x) = 4x - 8$?

Accepted Answer

$f^{-1}(x) = \dfrac{x - 8}{4}$

Question 9

Given $f(x) = x^2 - 4x + 1$ and $g(x) = 2x^2 + 5x + 1$, find $(f + g)(2)$.

Accepted Answer

$15$

Question 10

Solve for $x$: $\sqrt{2x + 3} = 7$

Accepted Answer

$x = 23$

Question 11

Which of the following is the correct solution to $0.8^x = 4$? (Round to the nearest hundredth)

Accepted Answer

$x = -7.22$

Question 12

If $25,000$ is invested at an annual interest rate of $2.5\%$ compounded quarterly, how much will be in the account after $25$ years? (Round to the nearest cent)

Accepted Answer

$A = 43,000.77$

Question 13

Which of the following is the correct equation for the vertical asymptote of $f(x) = \dfrac{x-1}{x^2-3}$?

Accepted Answer

$x = \pm \sqrt{3}$

Question 14

Which function best models data that increases rapidly and then levels off, as seen in population growth with limited resources?

Accepted Answer

Logarithmic

Question 15

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

Accepted Answer

$x = 4$

Question 16

Which of the following is the correct exponential form of $\sqrt[3]{x^7}$?

Accepted Answer

$x^{7/3}$

Question 17

Given the system: $\begin{cases} -3x + 2y = 11 \ x - y = -3 \end{cases}$, what is the solution?

Accepted Answer

$(-1, -4)$

Question 18

Which of the following is the correct result of $(3 - 5i)(2 - 4i)$ in standard form $a + bi$?

Accepted Answer

$-14 + 22i$

Question 19

If $f(x) = (x-2)^2 - 7$, what are the coordinates of the vertex?

Accepted Answer

$(2, -7)$

Question 20

Which of the following best describes the range of the function $f(x) = \sqrt{x-4}$?

Accepted Answer

$[0, \infty)$

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