Question 1

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$1$$?

Accepted Answer

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

Question 2

Given the equation $$x^2$$ + $$(y-1)^2 = 9$, what are the center and radius of the circle?

Accepted Answer

Center: $$(0, 1)$$, Radius: $$3$$

Question 3

Which of the following is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 4

What is the slope of the line passing through the points $$(-1, 1)$$ and $$(4, 3)$$?

Accepted Answer

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

Question 5

Which of the following best describes the domain of $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 6

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

Accepted Answer

$$[8, \infty)$$

Question 7

Which transformation is represented by $$f(x-3) + 2$$?

Accepted Answer

Shift right 3 units, up 2 units

Question 8

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

Accepted Answer

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

Question 9

Which of the following describes the range of $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 10

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

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 11

Which of the following is the equation of a line parallel to $$y = 2x - 6$$ passing through $$(-1, 4)$$?

Accepted Answer

Question 12

Given $$f(x) = \sqrt{x}$$ and $$g(x) = 3x - 6$$, what is the domain of $$f \cdot g$$?

Accepted Answer

$$[0, \infty)$$

Question 13

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

Accepted Answer

$$\sqrt{(x-2)^2$}$$

Question 14

If a function $$f(x) is $$reflected over the $$x-$$axis and then shifted down 2 units, which equation represents the transformation?

Accepted Answer

$$-f(x) - 2$$

Question 15

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

Accepted Answer

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

Question 16

What is the $$y-$$intercept of the line $$3x + 2y - 6 = 0$$?

Accepted Answer

$$(0, 3)$$

Question 17

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 18

If $$f(x) = x^2$ and g(x) = x - 1$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$4$$

Question 19

Which of the following is the correct decomposition of $$h(x) = \sqrt{x-2} as$$ $$f(g(x))$$?

Accepted Answer

$$f(x) = \sqrt{x},\ g(x) = x-2$$

Graphs and Functions: Foundations for College Algebra

Study Guide - Practice Questions