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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