Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input has at most one output.

Question 2

Given the relation $$\{(-3, 5), (0, 2), (3, 5)\}$$, what are the inputs and outputs, and is it a function?

Accepted Answer

Inputs: $$-3, 0, 3$$; Outputs: $$5, 2, 5$$; Function

Question 3

Which equation represents a function?

Accepted Answer

$$y = -2x + 10$$

Question 4

What is the domain of the function $$f(x) = \sqrt{x+4}$$? Express your answer in interval notation.

Accepted Answer

$$[-4, \infty)$$

Question 5

Which of the following is the correct interval notation for the range of the function $$f(x)$$ shown in the left graph of image 2?

Accepted Answer

$$[-1, 2)$$

Question 6

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (f+g)(x$$)$$ and its domain?

Accepted Answer

$$(f+g)(x) = x^2$ + x + 1$$, domain: $$(-\infty, \infty)$$

Question 7

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

Accepted Answer

Shift right 3 units, up 2 units

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Which of the following equations is NOT a circle?

Accepted Answer

$$x^3$$ + $$y^2 + 4x - 8y + 4 = 0$

Question 11

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, find (f$$ \circ g)(x)$$ and its domain.

Accepted Answer

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

Question 12

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

Accepted Answer

The graph is stretched vertically.

Question 13

Given the line $$3x + 2y - 6 = 0$$, what is its slope and y-intercept?

Accepted Answer

Slope: $$-\frac{3}{2}$$, y-intercept: $$3$$

Question 14

If $$f(x) = x^2$ + 4$$ and $$g(x) = 5x + 7$$, what is $$(f+g)(x)$$?

Accepted Answer

$$x^2 + 5x + 11$

Question 15

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

Accepted Answer

Reflection over the x-axis

Question 16

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

Accepted Answer

$$g(f(x)) = x^2$ - 2$$

Question 17

Which of the following is the correct set builder notation for the domain $$[-4, 5)$$?

Accepted Answer

$$\{x | -4 \leq x \u003c 5\}$$

College Algebra Study Guide: Functions, Graphs, and Transformations

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