Functions worked
- 1. Unit 2: FunctionsUnit 2: Functions
- 2. What do we need to do orWhat do we need to do or change for Unit 2?change for Unit 2? Things to keep:Things to keep: Things to change:Things to change:
- 3. TranslationsTranslations First, you have to know what the parentFirst, you have to know what the parent functions look like!functions look like! Parent functions…Parent functions…
- 6. We did this in Alg 2!We did this in Alg 2! Graph the parent function and move it!Graph the parent function and move it! Ex:Ex: Left or right?Left or right? Up or down?Up or down? Flip or normal?Flip or normal? 2 ( 4) 5y x= − − +
- 7. New to Pre-Calc…New to Pre-Calc… -f(x)-f(x) If there is a negative in the front it is aIf there is a negative in the front it is a reflection over the x-axis. (flip)reflection over the x-axis. (flip) f(-x)f(-x) If there is a negative on theIf there is a negative on the “inside” it is a“inside” it is a reflection over the y-axis. (mirror imaged)reflection over the y-axis. (mirror imaged)
- 8. GraphGraph Exponential ExampleExponential Example Log ExampleLog Example 1 2 5x y − = + log( 5) 1y x= − +
- 9. Practice GraphingPractice Graphing 2 1y x= − + − ( ) 3 3 1y x= − − − +
- 10. SymmetrySymmetry
- 11. Symmetry - ExamplesSymmetry - Examples w/ respect to the y-axisw/ respect to the y-axis (EVEN)(EVEN) f(x) = xf(x) = x22 w/ respect to the x-axisw/ respect to the x-axis (ODD)(ODD) x = yx = y22 w/ respect to the originw/ respect to the origin f(x) = xf(x) = x33
- 14. Symmetry -Symmetry - algebraicallyalgebraically 1.1. 2.2. 3.3. 3)( 2 −= xxf 22)( 2 −−= xxxf 2 3 4 )( x x xf − =
- 15. HomeworkHomework P. 99 (47-54, 63-66P. 99 (47-54, 63-66 state endstate end behavior using limits toobehavior using limits too)) p. 109 (29-31p. 109 (29-31 no calc…justno calc…just graphgraph, 35, 38, 39, 41), 35, 38, 39, 41)