Algebra II : Absolute Value

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #6 : 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 .

Example Question #7 : Graphing Absolute Value Functions

Which of the following absolute value functions is represented by the following 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:

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