1. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions TerminologyDefinitionIllustration Type of Symmetry of Graph f is an even function f(-x) = f(x)y = f(x) = x 2 with respect to the y - axis f is an odd function f(-x) = -f(x)y = f(x) = x 3 with respect to the origin

2. Precalculus Functions & Graphs Example 2.5A Graphs of Functions Determine whether f is even, odd or neither. Replace x with –x. So f is not even So f is not odd Therefore f is neither even nor odd.

3. Precalculus Functions & Graphs You Try #1 2.5A Graphs of Functions Determine whether f is even, odd or neither. Not even Odd A)Odd B)Even C)Neither The answers will appear after you have had a chance to work the problem.

4. Precalculus Functions & Graphs You Try #2 2.5A Graphs of Functions Determine whether f is even, odd or neither. Even A)Odd B)Even C)Neither The answers will appear after you have had a chance to work the problem.

5. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions Consider the graph. What happens to the graph when we add or subtract a constant from f(x)? Link So adding a constant k shifts the graph vertically upward a distance of k. So subtracting a constant k shifts the graph vertically downward a distance of k.

6. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions Consider the graph. What happens to the graph when we add or subtract a constant from x? So subtracting a constant h from x shifts the graph horizontally to the right a distance of h. So adding a constant h to x shifts the graph horizontally to the left a distance of h. Link

7. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions Consider the graph. What happens to the graph when we multiply f(x) by a constant? Link So multiplying f(x) by a constant a, vertically stretches the graph by a factor of a. So multiplying f(x) by a constant a, vertically compresses the graph by a factor of 1/a. Multiplying f(x) by a negative reflects the graph over the x axis.

8. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions Consider the graph. What happens to the graph when we multiply x by a constant? So multiplying x by a constant b, horizontally compresses the graph by a factor of b. So multiplying f(x) by a constant b, horizontally stretches the graph by a factor of 1/b. Link

9. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions Parent Functions

10. Precalculus Functions & Graphs Notes 2.5A Graphs of Functions Parent Functions

11. Precalculus Functions & Graphs You Try #3 2.5A Graphs of Functions Sketch on the same coordinate plane, the graphs of f, for the given values of c. This is not a Quizdom problem.

12. Precalculus Functions & Graphs You Try #4 2.5A Graphs of Functions Sketch on the same coordinate plane, the graphs of f, for the given values of c. This is not a Quizdom problem.

13. Precalculus Functions & Graphs You Try #5 2.5A Graphs of Functions Sketch on the same coordinate plane, the graphs of f, for the given values of c. This is not a Quizdom problem.