Q: What is the end behavior of the function $$f(x) = x^4$ + x^3$ - x + 1$$?

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

Question 1

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

Accepted Answer

$$8$$

Question 2

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

Accepted Answer

$$[2, \infty)$$

Question 3

Given the equation $$x = 4$$, which of the following best describes its graph?

Accepted Answer

A vertical line passing through $$x = 4$$

Question 4

Find the slope-intercept form of the line passing through the points $$(6, -3)$$ and $$(3, 2).$$

Accepted Answer

Question 5

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

Accepted Answer

$$(4, \infty)$$

Question 6

For the function $$f(x) = |x-3| - 4$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[-4, \infty)$$

Question 7

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

Accepted Answer

$$[-5, 4]$$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

$$x = 2 \pm 4i$$

Question 10

What is the end behavior of the function $$f(x) = x^4$ + x^3$ - x + 1$$?

Accepted Answer

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

Question 11

Solve the polynomial equation $$x^3$$ + $$x^2 - 4x - 4 = 0$.

Accepted Answer

Question 12

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

Accepted Answer

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

Question 13

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 14

Find the inverse function $$f^{-1}(x$$)$$ for f(x) = 2x - 7$.

Accepted Answer

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

Question 15

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

$$A \approx 3582.13$$

Question 16

Find $$\log_2$ 64.$$

Accepted Answer

$$6$$

Question 17

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

Accepted Answer

$$x \approx -1.013$$

Question 18

Let $$f(x) = -2(x+1)^3$ - 3. $$What is the domain and range of $$f$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 19

Find $$\log_5$ 411$$ rounded to the nearest hundredth.

Accepted Answer

$$3.54$$

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