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2.7 ABSOLUTE VALUE FUNCTIONS AND GRAPHS
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ABSOLUTE VALUE FUNCTION
The simplest form (parent graph) of an absolute value function is f x x
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ABSOLUTE VALUE FUNCTION
The graph of is V-shaped and symmetric about a vertical line called the axis of symmetry. The graph also has a single maxima point or minima
point, called a vertex
f x x
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TRANSFORMATIONS OF THE ABSOLUTE VALUE FUNCTION
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EXAMPLEMake a table of values, then graph the function. Describe the transformation from the parent function.
4y x
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EXAMPLEMake a table of values, then graph the function. Describe the transformation from the parent function. 2 3f x x
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EXAMPLEGraph the equation. Describe the transformation from the parent function.
1
2y x
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EXAMPLEGraph the equation. Describe the transformation from the parent function.
2y x
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GENERAL FORM OF THE ABSOLUTE VALUE FUNCTION
When translations, stretches and compressions are combined for Absolute Value Functions, we derive the general form:
The stretch or compression factor is |a|, the vertex is located at (h, k), and the axis of symmetry is the line x = h
y a x h k
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EXAMPLEWithout graphing, what are the vertex and axis of symmetry of the graph of:
3 2 4y x
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EXAMPLEWithout graphing, what are the vertex and axis of symmetry of the graph of:
2 1 3y x
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WRITING AN ABSOLUTE VALUE FUNCTION FROM A GRAPH
1. Identify the vertex2. Identify a, by finding the slope of the
branch on the right 3. Write the equation
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EXAMPLEWhat is the equation of the absolute value function?
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EXAMPLEWhat is the equation of the absolute value function?