Functions

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)