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^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 is NOT a function?

Accepted Answer

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

Question 4

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

Accepted Answer

$$[-4, \infty)$$

Question 5

A line passes through the points $$(-1, 1)$$ and $$(4, 3). $$What is its slope?

Accepted Answer

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

Question 6

Which transformation shifts the graph of $$f(x)$$ right by $$3$$ units and up by $$2$$ units?

Accepted Answer

$$f(x-3) + 2$$

Question 7

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

Accepted Answer

$$[8, \infty)$$

Question 8

Which of the following best describes the effect of multiplying a function $$f(x) by a $$constant $$c \u003e 1$$?

Accepted Answer

Vertical stretch

Question 9

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

Accepted Answer

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

Question 10

Which equation represents a line perpendicular to $$y = 2x - 6$$ and passing through $$(-1, 4)$$?

Accepted Answer

$$y - 4 = -\frac{1}{2}(x + 1)$$

Question 11

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

Accepted Answer

$$4$$

Question 12

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 13

If $$f(x) = \sqrt{x+4} + 30$$ and $$g(x) = \sqrt{x+4} - 2x + 35$$, what is the domain of $$(f-g)(x)$$?

Accepted Answer

$$[-4, \infty)$$

Question 14

Which of the following describes the transformation $$g(x) = -f(x-3) + 2$$ applied to $$f(x)$$?

Accepted Answer

Reflect over x-axis, shift right 3 units, up 2 units

Question 15

Given $$h(x) = 2x^3$ - 4$$ and $$k(x) = x^2$ + 2$$, what is $$h \cdot k(x)$$?

Accepted Answer

$$2x^5$$ + $$4x^3$$ - $$4x^2 - 8$

Question 16

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: College Algebra Study Guide

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