Q: Find the domain of $$P(x) = \\frac{-x}{\\sqrt{x^2$ - 2}}.$$

$$x \\leq -\\sqrt{2} or$$ $$x \\geq \\sqrt{2}$$

Question 1

Solve the inequality $$-3 \leq 3 - 2x \u003c 9$$ and express the solution set in interval notation.

Accepted Answer

$$[-3, 6]$$

Question 2

Find the domain of the function $$f(x) = \sqrt{3x + 6}.$$

Accepted Answer

$$x \geq -2$$

Question 3

Given $$f(x) = -3x^2$ + 5x$$, what is the $$y-$$intercept of the graph of $$f$$?

Accepted Answer

$$y = 5$$

Question 4

If $$f(x) = x^2$ - 2$$, what is $$f(0)$$ and what point is on the graph of $$f$$?

Accepted Answer

$$f(0) = -2$$, point $$(0, -2)$$

Question 5

Find the zeros of $$f(x) = x^2$ + 4.$$

Accepted Answer

$$x = \pm 2i$$

Question 6

Given $$f(x) = \frac{x^4$ + 2}{x}$$, what is the domain of $$f$$?

Accepted Answer

$$x \neq 0$$

Question 7

Find the domain of $$P(x) = \frac{-x}{\sqrt{x^2$ - 2}}.$$

Accepted Answer

$$x \leq -\sqrt{2} or$$ $$x \geq \sqrt{2}$$

Question 8

Let $$f(x) = 1 + \frac{1}{x}$$ and $$g(x) = \frac{4}{x - 1}. $$Find $$\left(\frac{f}{g}\right)(x).$$

Accepted Answer

$$\frac{x(x-1) + 1}{4(x-1)}$$

Question 9

Given $$f(x) = 3x^2$ - 2x + 6$$, find the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$6x + 3h - 2$$

Question 10

Suppose $$f(x) is $$decreasing on $$(-3, 5). $$What can be said about the graph of $$y = -f(x) on$$ $$(-3, 5)$$?

Accepted Answer

It is increasing on $$(-3, 5)$$

Question 11

Find the average rate of change of $$f(x) = x^2$ - 2x + 1$$ from $$x = -3 to$$ $$x = -2.$$

Accepted Answer

$$-5$$

Question 12

A company models its profit by $$P(x) = -2x^2$ + 3x + 5$$, where $$x is $$the number of units sold. What is the maximum profit, and for how many units is it achieved?

Accepted Answer

Maximum profit is $$6.125 at$$ $$x = 0.75$$

Question 13

Given the function $$f(x) = \sqrt{x}$$, what is the equation after shifting left 2 units and up 3 units?

Accepted Answer

$$f(x) = \sqrt{x+2} + 3$$

Question 14

If two lines are perpendicular and one has slope $$m_1 = 2$, what is the slope m_2$ of the other?

Accepted Answer

$$m_2$$ = -\frac{1}{2}$$

Question 15

Find the domain of $$g(x) = \frac{3x}{x^2$ - 9}.$$

Accepted Answer

$$x \neq 3, x \neq -3$$

Question 16

Given $$f(x) = x^3$ + 5$$, determine whether $$f(x) is $$even, odd, or neither.

Accepted Answer

Neither

Question 17

Let $$f(x) = \frac{x}{x+1}$$, find $$f(f(x)).$$

Accepted Answer

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

Question 18

Find the $$x-$$intercept of the function $$y = \frac{2}{x} + 3.$$

Accepted Answer

$$x = \frac{2}{3}$$

Question 19

Given $$f(x) = x^2$ - 2x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(1, 2)$$

Precalculus Study Guide: Functions, Graphs, and Algebraic Techniques

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