Q: Which of the following best describes the end behavior of $$f(x) = x^4$ + x^3$ - x + 1$$?

$$f(x) \to \infty as$$ $$x \to \infty$$ and $$f(x) \to \infty as$$ $$x \to -\infty$$

Question 1

Evaluate $$f(-1)$$ for the function $$f(x) = 7x^2$ - 3x + 2.$$

Accepted Answer

Question 2

Which of the following best describes the domain of the function $$f(x) = \frac{-2}{x+2} + 3$$?

Accepted Answer

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

Question 3

Solve the inequality $$3(x-3) + 1 \u003e 5(x-2). $$Express your answer in interval notation.

Accepted Answer

$$(-\infty, 4)$$

Question 4

Given $$f(x) = 2x^2$ - 12x + 12$$, rewrite $$f(x) in $$vertex form by completing the square.

Accepted Answer

$$f(x) = 2(x-3)^2$ - 6$$

Question 5

What is the minimum value of $$f(x) = 2x^2$ - 12x + 12$$?

Accepted Answer

$$-6$$

Question 6

Solve the quadratic equation $$x^2 - 4x + 16 = 0$.

Accepted Answer

$$x = 2 \pm 4i$$

Question 7

Let $$f(x) = 3x - 4$$ and $$g(x) = 2x - 5. $$Find $$(fg)(x).$$

Accepted Answer

$$6x^2 - 23x + 20$

Question 8

Let $$f(x) = x^5$ + 7$$ and $$g(x) = \sqrt{\frac{x-2}{5}}. $$Find $$(f \circ g)(x).$$

Accepted Answer

$$\left(\sqrt{\frac{x-2}{5}}\$$right)^5$$ + 7$$

Question 9

Find the inverse of the function $$f(x) = 2x - 7.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x+7}{2}$$

Question 10

Suppose $$2000 is invested at 6\%$$ annual interest compounded quarterly. How much money would you have in 9 years? Use $$A = P\left(1 + \frac{r}{n}\$$right)^{nt}$$.

Accepted Answer

$$A \approx 3440.90$$

Question 11

Solve the absolute value inequality $$|2x + 1| \leq 9. $$Express your answer in interval notation.

Accepted Answer

$$[-5, 4]$$

Question 12

Find $$\log_2$ 64.$$

Accepted Answer

$$6$$

Question 13

Find $$\log_5$ 411. $$Round your answer to the nearest hundredth.

Accepted Answer

$$3.57$$

Question 14

Solve the exponential equation $$9^{8x}$$ = $$5^{x-6}. $$Round your answer to three decimal places.

Accepted Answer

$$x \approx -0.370$$

Question 15

Which of the following best describes the end behavior of $$f(x) = x^4$ + x^3$ - x + 1$$?

Accepted Answer

$$f(x) 	o \infty as$$ $$x 	o \infty$$ and $$f(x) 	o \infty as$$ $$x 	o -\infty$$

Question 16

Find all real solutions to the cubic equation $$x^3$$ + $$x^2 - 4x - 4 = 0$.

Accepted Answer

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

Question 17

For the function $$f(x) = |x-3| - 4$$, what is the vertex of the graph?

Accepted Answer

$$(3, -4)$$

Question 18

Which of the following intervals describes where the function $$f(x) = 2x^2$ - 12x + 12 is $$increasing?

Accepted Answer

$$(3, \infty)$$

Question 19

A patient’s medication level in the bloodstream is modeled by $$f(t) = 3t + 2 - 4$$, where $$t is $$hours after administration. What is the initial medication level?

Accepted Answer

$$1$$

Question 20

Which of the following is the range of $$f(x) = -2(x+1)^3$ - 3$$?

Accepted Answer

$$(-\infty, \infty)$$

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