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# 2.7

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### 2.7

1. 1. 2.7 ABSOLUTE VALUE FUNCTIONS AND GRAPHS
2. 2. ABSOLUTE VALUE FUNCTION <ul><li>The simplest form (parent graph) of an absolute value function is </li></ul>
3. 3. ABSOLUTE VALUE FUNCTION <ul><li>The graph of is V-shaped and symmetric about a vertical line called the axis of symmetry . </li></ul><ul><ul><li>The graph also has a single maxima point or minima point, called a vertex </li></ul></ul>
4. 4. TRANSFORMATIONS OF THE ABSOLUTE VALUE FUNCTION
5. 5. EXAMPLE <ul><li>Make a table of values, then graph the function. Describe the transformation from the parent function. </li></ul>
6. 6. EXAMPLE <ul><li>Make a table of values, then graph the function. Describe the transformation from the parent function. </li></ul>
7. 7. EXAMPLE <ul><li>Graph the equation. Describe the transformation from the parent function. </li></ul>
8. 8. EXAMPLE <ul><li>Graph the equation. Describe the transformation from the parent function. </li></ul>
9. 9. 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
10. 10. EXAMPLE <ul><li>Without graphing, what are the vertex and axis of symmetry of the graph of: </li></ul>
11. 11. EXAMPLE <ul><li>Without graphing, what are the vertex and axis of symmetry of the graph of: </li></ul>
12. 12. WRITING AN ABSOLUTE VALUE FUNCTION FROM A GRAPH <ul><li>Identify the vertex </li></ul><ul><li>Identify a, by finding the slope of the branch on the right </li></ul><ul><li>Write the equation </li></ul>
13. 13. EXAMPLE <ul><li>What is the equation of the absolute value function? </li></ul>
14. 14. EXAMPLE <ul><li>What is the equation of the absolute value function? </li></ul>