Question 1

Which of the following equations is equivalent to $$|2x - 3| = 11$$?

Accepted Answer

$$2x - 3 = 11 or$$ $$2x - 3 = -11$$

Question 2

Solve the equation $$x^{\frac{2}$${3}} - \frac{3}{4} = -\frac{1}{2}$$ for x$.

Accepted Answer

$$x = 1$$

Question 3

Which of the following is the correct interval notation for the solution to $$3 - 2x \leq 11$$?

Accepted Answer

$$(-\infty, -4]$$

Question 4

If $$f(x) = x^2$ + 3$$, what is $$f(-x)$$?

Accepted Answer

$$x^2 + 3$

Question 5

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

Accepted Answer

$$[0, \infty)$$

Question 6

Which of the following describes the transformation from $$y = x^2$ to y$$ = $$5x^2$$?

Accepted Answer

Vertical stretch by a factor of 5

Question 7

If $$f(x) = x^2$ + 2x$$, what is the average rate of change from $$x = 3 to$$ $$x = 5$$?

Accepted Answer

$$9$$

Question 8

Which of the following is the equation of a line passing through $$(2, -1)$$ and parallel to $$y = \frac{2}{3}x - 2$$?

Accepted Answer

$$y = \frac{2}{3}x - \frac{7}{3}$$

Question 9

Given the graph of $$f(x) = x^2$ - 4 ($$see image), what is the range of the function?

Accepted Answer

$$[-4, \infty)$$

Question 10

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 11

If $$f(x) = x^2$ + 1$$ and $$g(x) = 1 - 4x$$, what is $$g(x + 2)$$?

Accepted Answer

$$1 - 4(x + 2)$$

Question 12

Which of the following is the correct difference quotient for $$f(x) = x^2$ - 4x + 7$$?

Accepted Answer

$$\frac{f(x + h) - f(x)}{h}$$

Question 13

Which of the following is the equation of a vertical line passing through $$(3, -2)$$?

Accepted Answer

$$x = 3$$

Question 14

Given the compound inequality $$-2 \u003c 5 + 3x \u003c 20$$, what is the solution in interval notation?

Accepted Answer

$$(-\frac{7}{3}, 5)$$

Question 15

Which of the following describes the transformation from $$y = x^3$ to y$$ = \frac{1}{3}(x + $$6)^3$$?

Accepted Answer

Shift left 6 units and vertical shrink by a factor of $$\frac{1}{3}$$

Question 16

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$

Question 17

Given the graph of $$y = g(x) ($$see image), what is the value of $$g(-4)$$?

Accepted Answer

$$3$$

Question 18

Which of the following is the correct solution set for $$|x - 4| \u003c 3$$?

Accepted Answer

$$(1, 7)$$

Question 19

If the slope of a line is $$m = -\frac{3}{5}$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$\frac{5}{3}$$

Question 20

Which of the following is the correct interpretation of the average rate of change of a function $$f$$ from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$\frac{f(x_2$) - f(x_1$)}{x_2$ - x_1$}$$

Precalculus Study Notes: Equations, Inequalities, and Functions

스터디 가이드 - 연습 문제