Question 1

Which of the following graphs represents a function that is symmetric with respect to the y-axis?

Accepted Answer

The graph of $$y = |x|$$

Question 2

Given the graph of $$y = \frac{1}{x}$$, which of the following statements is true?

Accepted Answer

The graph has vertical and horizontal asymptotes at $$x = 0$$ and $$y = 0.$$

Question 3

Which graph shows a function that is NOT one-to-one?

Accepted Answer

The graph of $$y = x^2$

Question 4

Which of the following graphs represents a function with domain $$[0, \infty)$$ and range $$[0, \infty)$$?

Accepted Answer

The graph of $$y = \sqrt{x}$$

Question 5

Which graph represents a function that is symmetric with respect to the origin?

Accepted Answer

The graph of $$y = x^3$

Question 6

Which graph shows a function with a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 4$$?

Accepted Answer

The graph of $$y = \frac{1}{x-2} + 4$$

Question 7

Which of the following graphs represents a piecewise function?

Accepted Answer

A graph with a parabola for $$x \u003c 1$$ and a line for $$x \geq 1$$

Question 8

Which graph represents the transformation of $$y = x^2$ shifted right 2 units and up 3 units?

Accepted Answer

The graph of $$y = (x-2)^2$ + 3$$

Question 9

Which graph shows a function with domain $$(-\infty, 2) \cup (2, \infty)$$ and range $$(-\infty, 4) \cup (4, \infty)$$?

Accepted Answer

The graph of $$y = \frac{1}{x-2} + 4$$

Question 10

Which graph represents the function $$y = |x|$$?

Accepted Answer

A V-shaped graph opening upward with vertex at the origin

Question 11

Which graph represents a circle centered at $$(0,1)$$ with radius $$3$$?

Accepted Answer

The graph of $$x^2$$ + $$(y-1)^2 = 9$

Question 12

Which graph shows a function with a vertex at $$(3,12)$$ and no real $$x-$$intercepts?

Accepted Answer

The graph of $$y = 3(x-3)^2$ + 12$$

Question 13

Which graph represents the function $$y = \sqrt{x}$$?

Accepted Answer

A curve starting at the origin and increasing slowly to the right

Question 14

Which graph represents the function $$y = x^3$?

Accepted Answer

An S-shaped curve passing through the origin

Question 15

Which graph represents the function $$y = \sqrt[3]{x}$$?

Accepted Answer

A curve passing through the origin, increasing slowly to the right and left

Question 16

Which graph represents the function $$y = |x+4|$$ reflected over the $$x-$$axis and shifted down 2 units?

Accepted Answer

The graph of $$y = -|x+4| - 2$$

Question 17

Which graph represents the function $$y = \sqrt{-x+2} - 3$$?

Accepted Answer

A curve starting at $$(2,-3)$$ and increasing to the left

Question 18

Which graph represents the function $$y = (x+4)^3$?

Accepted Answer

An S-shaped curve passing through $$(-4,0)$$

College Algebra Comprehensive Study Notes: Equations, Functions, Graphs, and Applications

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