Question 1

Which equation represents a circle with center at $$(2, -3)$$ and radius $$4$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 16$

Question 2

Given the equation $$x^2$$ + $$y^2 - 2x + 4y - 4 = 0$, what is the center and radius of the circle?

Accepted Answer

Center: $$(1, -2)$$, Radius: $$3$$

Question 3

Which of the following relations is NOT a function?

Accepted Answer

{$$(2, 5), (0, 2), (2, 9)$$}

Question 4

What is the domain of the function $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 5

Find the slope of the line passing through the points $$(-1, 1)$$ and $$(4, 3).$$

Accepted Answer

$$\frac{2}{5}$$

Question 6

Which of the following equations represents a vertical line?

Accepted Answer

$$x = 3$$

Question 7

Given $$y = -2x + 10$$, rewrite in function notation and evaluate at $$f(3).$$

Accepted Answer

$$f(x) = -2x + 10$$, $$f(3) = 4$$

Question 8

What is the domain of $$f(x) = \frac{1}{x^2$ - 5x + 6}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 9

Which transformation represents a vertical stretch of the function $$f(x) by a $$factor of $$c$$?

Accepted Answer

$$c \cdot f(x)$$

Question 10

If $$f(x) = x^2$ and g(x$$) = \sqrt{x - 8}$$, what is (f$$ \circ g)(x)$$ and its domain?

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x - 8})^2$ = x - 8$$, Domain: $$[8, \infty)$$

Question 11

Which of the following is the correct point-slope form for a line with slope $$-\frac{2}{5}$$ passing through $$(1, 3)$$?

Accepted Answer

$$y - 3 = -\frac{2}{5}(x - 1)$$

Question 12

Given the function $$f(x) = |x|$$, which transformation results in $$g(x) = -4|x|$$?

Accepted Answer

Reflection over the x-axis and vertical stretch by 4

Question 13

What is the domain and range of $$f(x) = x^2$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[0, \infty)$$

Question 14

If $$f(x) = x^2$ + \frac{1}{x}$$ and $$g(x) = x^2$ + x + 2$$, what is $$f(x) + g(x)$$?

Accepted Answer

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

Question 15

Which of the following is the correct composite function $$(f \circ g)(x)$$ for $$f(x) = \sqrt{x+4}$$ and $$g(x) = (x-2)^2$ - 4$$?

Accepted Answer

Question 16

Which of the following is the correct standard form for the equation $$x^2$$ + $$y^2 + 2x + 6y + 8 = 0$?

Accepted Answer

$$(x+1)^2$$ + $$(y+3)^2 = 2$

Question 17

If $$f(x) = x^3$ is reflected over the x-axis and then shifted down 2 units, what is the equation for the transformed function h(x$$)$$?

Accepted Answer

$$h(x) = -x^3$ - 2$$

Question 18

Which of the following is the correct domain for $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Graphs and Functions: Study Notes for College Algebra

Study Guide - Practice Questions