Algebra II : Graphing Absolute Value Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #76 : Absolute Value

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

Correct answer:

Explanation:

Below is the graph of :

Axes_1

The given graph is the graph of  reflected in the -axis, then translated up 6 units. This graph is 

, where .

The function graphed is therefore

Example Question #77 : Absolute Value

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

Correct answer:

Explanation:

Below is the graph of :

Axes_1

The given graph is the graph of  reflected in the -axis, then translated left 2 units (or, equivalently, right  units. This graph is 

, where .

The function graphed is therefore

Example Question #78 : Absolute Value

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

The correct answer is not given among the other responses.

Correct answer:

Explanation:

Below is the graph of :

Axes_1

The given graph is the graph of   translated by moving the graph 7 units left (that is,  unit right) and 2 units down (that is,  units up)

The function graphed is therefore

 where . That is,

Example Question #79 : Absolute Value

Screen_shot_2014-12-24_at_3.03.30_pm

What is the equation of the above function?

Possible Answers:

Correct answer:

Explanation:

The formula of an absolute value function is  where m is the slope, a is the horizontal shift and b is the vertical shift. The slope can be found with any two adjacent integer points, e.g.  and , and plugging them into the slope formula, , yielding . The vertical and horizontal shifts are determined by where the crux of the absolute value function is. In this case, at , and those are your a and b, respectively.

Example Question #80 : Absolute Value

Which of the following absolute value functions is represented by the above graph?

Possible Answers:

The equation cannot be determined from the graph.

Correct answer:

Explanation:

The equation can be determined from the graph by following the rules of transformations; the base equation is:

The graph of this base equation is:

When we compare our graph to the base equation graph, we see that it has been shifted right 3 units, up 1 unit, and our graph has been stretched vertically by a factor of 2. Following the rules of transformations, the equation for our graph is written as:

Example Question #1 : Graphing Absolute Value Functions

Give the vertex of the graph of the function .

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

Let 

The graph of this basic absolute value function is a "V"-shaped graph with a vertex at the origin, or the point with coordinates . In terms of ,

The graph of this function can be formed by shifting the graph of  left 6 units ( ) and down 7 units (). The vertex is therefore located at .

Example Question #2 : Graphing Absolute Value Functions

Give the vertex of the graph of the function .

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

Let 

The graph of this basic absolute value function is a "V"-shaped graph with a vertex at the origin, or the point with coordinates . In terms of ,

or, alternatively written,

The graph of  is the same as that of , after it shifts 10 units left (  ), it flips vertically (negative symbol), and it shifts up 10 units (the second ). The flip does not affect the position of the vertex, but the shifts do; the vertex of the graph of  is at .

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