Question 1

Let $$A = \{-5, -2, 0, 2.5\}$$ and $$B = \{-5, -1.0, 1.5\}. $$What is $$A \cap B$$?

Accepted Answer

$$\{-5\}$$

Question 2

Simplify the following expression: $$\left( \dfrac{7x^4$ y^3$}{2x^2$ y^5$} \$$right)^{-2}$$

Accepted Answer

Question 3

Find the solution set of $$\dfrac{\sqrt{x-4}}{x-2} = 1.$$

Accepted Answer

$$x = 5$$

Question 4

Solve the inequality $$3x^2 - 5x - 12$$ \geq 0$$. Write your answer in interval notation.

Accepted Answer

$$(-\infty, -1] \cup [4, \infty)$$

Question 5

Given points $$P(-4, -7)$$ and $$Q(1, 5)$$, what are the coordinates of the midpoint of $$\overline{PQ}$$?

Accepted Answer

$$(-1.5, -1)$$

Question 6

Find the center and radius of the circle with equation $$x^2 - 4x$$ + $$y^2 + 8y = 5$.

Accepted Answer

Center $$(2, -4)$$, radius $$3$$

Question 7

Given points $$(-3, -2)$$ and $$(15, 4)$$, what is the equation of the line passing through these two points in slope-intercept form?

Accepted Answer

Question 8

Determine whether the correspondence diagram on the left in the image is a function.

Accepted Answer

Yes, because each input has exactly one output.

Question 9

Given $$f(x) = \dfrac{7x}{x^2$ + x}$$, determine whether $$f(x) is $$odd, even, or neither.

Accepted Answer

Odd

Question 10

Let $$f(x) = 4|x| - 9. $$What is the $$y-$$intercept of $$f(x)$$?

Accepted Answer

$$(0, -9)$$

Question 11

Let $$f(x) = -\dfrac{1}{2}x$$ and $$g(x) = \sqrt{x-1}. $$What is $$(f \circ g)(9)$$?

Accepted Answer

$$-4$$

Question 12

Find the domain of $$(g \circ f)(x)$$ where $$f(x) = -\dfrac{1}{2}x$$ and $$g(x) = \sqrt{x-1}.$$

Accepted Answer

$$(-\infty, -2]$$

Question 13

Which of the following equations represents a circle with center at $$(0,0)$$ and radius $$10$$?

Accepted Answer

$$x^2$$ + $$y^2 = 100$

Question 14

Given the line $$y = \dfrac{1}{2}x + 3$$, which of the following lines is perpendicular to it?

Accepted Answer

$$y = -2x + 1$$

Question 15

For which value of $$x is $$the function $$f(x) = \dfrac{7x}{x^2$ + x}$$ undefined?

Accepted Answer

$$x = 0$$ and $$x = -1$$

Question 16

If $$f(x) = 4|x| - 9$$, for which interval is $$f(x)$$ decreasing?

Accepted Answer

$$(-\infty, 0)$$

Question 17

Which of the following best describes the transformation from $$y = |x| to$$ $$y = 4|x| - 9$$?

Accepted Answer

Vertical stretch by 4 and shift down by 9

Question 18

Given $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 19

Which of the following is the solution set for $$\dfrac{2x+3}{x-5} = 1$$?

Accepted Answer

$$x = 8$$

Precalculus Exam 1 Review: Sets, Functions, Equations, and Graphs

Study Guide - Practice Questions