Q: For the function $$f(x) = -2x^2$(x-3)(x+5)$$, what is the end behavior as $$x \to \infty$$ and $$x \to -\infty$$?

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

Question 1

What is the domain of the function $$f(x) = \sqrt{36 - 2x}$$?

Accepted Answer

$$(-\infty, 18]$$

Question 2

Given $$f(x) = \frac{5x}{x^2$ - 9}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 3

Solve for $$x$$: $$\sqrt{x + 7} - 1 = x$$

Accepted Answer

$$x = 2$$

Question 4

Find the inverse of $$f(x) = x^3$ + 3.$$

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x - 3}$$

Question 5

Given the piecewise function $$f(x) = \begin{cases} x^2$ + 2x - 1 & 	ext{if } x \geq 2 \ 3x + 1 & 	ext{if } x \u003c 2 \end{cases}$$, find $$f(5) - f(-5).$$

Accepted Answer

$$15$$

Question 6

For $$f(x) = 3x^2$ - x + 5$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$6x + 3h - 1$$

Question 7

Solve the quadratic equation: $$2x^2 - 1 = 3x$.

Accepted Answer

$$x = 2, x = -0.5$$

Question 8

Given $$f(x) = x^3$ + 5x^2$ - 8x + 2$$, which of the following is a zero of the function?

Accepted Answer

$$x = -1$$

Question 9

Solve the inequality $$2x^2 + 5x$$ \u003c 12$$ and write the solution in interval notation.

Accepted Answer

$$(-4, 1.5)$$

Question 10

Given $$f(x) = \frac{2}{x+1}$$ and $$g(x) = \frac{1}{x}$$, find $$(f \circ g)(x).$$

Accepted Answer

$$\frac{2}{\frac{1}{x} + 1}$$

Question 11

For the function $$f(x) = -2x^2$(x-3)(x+5)$$, what is the end behavior as $$x 	o \infty$$ and $$x 	o -\infty$$?

Accepted Answer

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

Question 12

Find the vertical asymptote of $$f(x) = \frac{x-2}{x^3$ - 5x}.$$

Accepted Answer

$$x = 0, x = \sqrt{5}, x = -\sqrt{5}$$

Question 13

Given the function $$f(x) = \frac{2x+4}{x^2$-25}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 5, x = -5$$

Question 14

For the quadratic function $$f(x) = -4x^2$ - 16x + 3$$, what is the maximum value and where does it occur?

Accepted Answer

Maximum at $$x = -2$$, $$f(-2) = 19$$

Question 15

Using the first graph provided, what is the range of $$f(x)$$?

Accepted Answer

$$[-2, 2]$$

Question 16

Using the first graph provided, on which interval is the function $$f(x)$$ increasing?

Accepted Answer

$$(-2, 2)$$

Question 17

Solve the logarithmic equation: $$\log_3$(x + 5) = 2.$$

Accepted Answer

$$x = 4$$

Question 18

Expand $$\log_b(x \sqrt{y^3$}).$$

Accepted Answer

$$\log_b x + \frac{3}{2} \log_b y$$

Question 19

Suppose you invest $$600 at 0.88% compounded quarterly for 4 years. Which formula gives the final amount A$?

Accepted Answer

$$A = 600(1 + \frac{0.0088}{4}$$)^{16}$$

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