Question 1

Which of the following relations is a function?

Accepted Answer

$$\{(2,5), (3,6), (4,7)\}$$

Question 2

Given the equation $$y^2 = x + 3$, is this equation a function of x$?

Accepted Answer

No, because some $$x$$ values correspond to more than one $$y$$ value.

Question 3

What is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 4

Which of the following graphs represents a function?

Accepted Answer

A graph where every $$x$$ value corresponds to exactly one $$y$$ value.

Question 5

Find the range of the function $$f(x) = x^2$ + 1.$$

Accepted Answer

$$[1, \infty)$$

Question 6

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

Accepted Answer

$$x^2 + x + 1$

Question 7

What is the domain of $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

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

Question 8

If $$f(x) = x^2$ and g(x) = 2x$, what is f(g(x$$))$$?

Accepted Answer

$$4x^2$$

Question 9

Which transformation results in the graph of $$f(x)$$ being reflected over the $$y-$$axis?

Accepted Answer

$$f(-x)$$

Question 10

What is the equation of a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x-2)^2$$ + $$(y+3)^2 = 25$

Question 11

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

Accepted Answer

$$(x-2)^2$$

Question 12

Which of the following describes a vertical shift of $$f(x) up by 3 $$units?

Accepted Answer

$$f(x) + 3$$

Question 13

If $$f(x) = \sqrt{x+4}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[-4, \infty)$$

Question 14

Which of the following is the result of reflecting $$f(x) = x^3$ over the x$-axis?

Accepted Answer

$$-x^3$$

Question 15

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

Accepted Answer

$$(x+2)^2$$

Question 16

Which of the following is the correct interval notation for all real numbers except $$x = 2$$?

Accepted Answer

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

Question 17

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

Accepted Answer

$$3x^3$$

Question 18

Which of the following is the standard form of the equation of a circle with center $$(1, -2)$$ and radius $$4$$?

Accepted Answer

$$(x-1)^2$$ + $$(y+2)^2 = 16$

Question 19

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

Accepted Answer

$$x^2 - x - 1$

College Algebra: Functions and Graphs (Study Guide)

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