Unit 2: FunctionsUnit 2: Functions

What do we need to do or What 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:

TranslationsTranslations First, you have to know what the parent First, you have to know what the parent

functions look like! functions look like! Parent functions…Parent functions…

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

New to Pre-Calc…New to Pre-Calc… -f(x)-f(x) If there is a negative in the front it is a If 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 the If there is a negative on the ““insideinside”” it is a it is a

reflection over the y-axis. (mirror imaged)reflection over the y-axis. (mirror imaged)

GraphGraph Exponential Example Exponential Example Log Example Log Example

12 5xy log( 5) 1y x

Practice GraphingPractice Graphing 2 1y x 33 1y x

SymmetrySymmetry

Symmetry - ExamplesSymmetry - Examples w/ respect to the y-axis w/ respect to the y-axis (EVEN)(EVEN)

f(x) = xf(x) = x22

w/ respect to the x-axis w/ respect to the x-axis (ODD)(ODD) x = yx = y22

w/ respect to the originw/ respect to the origin f(x) = xf(x) = x3 3

Symmetry - algebraicallySymmetry - algebraically

1.1.

2.2.

3.3.

3)( 2 xxf

22)( 2 xxxf

2

3

4)(

xxxf

HomeworkHomework

P. 99 (47-54, 63-66 P. 99 (47-54, 63-66 state end state end behavior using limits toobehavior using limits too))

p. 109 (29-31 p. 109 (29-31 no calc…just no calc…just graphgraph, 35, 38, 39, 41), 35, 38, 39, 41)