Q: Which of the following is the correct domain of the function $$f(x) = \dfrac{4-3x}{14-3x}$$?

$$\{x \mid x \neq \dfrac{14}{3}\}$$

Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7$$?

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 domain of the function $$f(x) = \dfrac{4-3x}{14-3x}$$?

Accepted Answer

$$\{x \mid x 
eq \dfrac{14}{3}\}$$

Question 2

Given the quadratic equation $$2x^2 - 8x + 3 = 0$, what are the solutions?

Accepted Answer

$$x = 2 \pm \dfrac{\sqrt{7}}{2}$$

Question 3

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^2$ - 7$$?

Accepted Answer

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

Question 4

A chemical solution is modeled by $$C(t) = 5e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 5e$$^{-1}$$ \approx 1.84 mg/L$$

Question 5

Solve the inequality $$\dfrac{x^2$}{x-2} \u003e 0$$ and express the solution in interval notation.

Accepted Answer

$$(0, 2) \cup (2, \infty)$$

Question 6

Which of the following is the correct factorization of $$x^2 - 6x + 5$?

Accepted Answer

$$(x-5)(x-1)$$

Question 7

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 8

Given $$f(x) = \sqrt{4 - x}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 4]$$

Question 9

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

Accepted Answer

$$(2x-1)^2 - 3(2x-1) + 2$

Question 10

Solve for $$x$$: $$\dfrac{2}{x} + \dfrac{3}{x+1} = 1$$

Accepted Answer

$$x = 1, x = -2$$

Question 11

Which of the following describes the range of $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 12

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 1.02$$ seconds

Question 13

Which of the following is the solution set for $$x^2 + 5x + 6$$ \leq 0$$?

Accepted Answer

$$[-3, -2]$$

Question 14

Divide $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using long division. What is the remainder?

Accepted Answer

$$-9$$

Question 15

Which of the following is the correct simplified form of $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

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

Question 16

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 17

Which of the following is the correct solution to the equation $$\sqrt{x+2} = x$$?

Accepted Answer

$$x = 2$$

Question 18

A rational function $$f(x) = \dfrac{2x+1}{x-4}$$ has which of the following vertical and horizontal asymptotes?

Accepted Answer

Vertical: $$x = 4$$, Horizontal: $$y = 2$$

Question 19

Which of the following intervals describes where the function $$f(x) = x^2$ - 4x + 3 is $$decreasing?

Accepted Answer

$$(-\infty, 2)$$

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