Functions worked
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Transcript of Functions worked
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Unit 2: FunctionsUnit 2: Functions
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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:
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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…
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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
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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)
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GraphGraph Exponential Example Exponential Example Log Example Log Example
12 5xy log( 5) 1y x
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Practice GraphingPractice Graphing 2 1y x 33 1y x
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SymmetrySymmetry
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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
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Symmetry - algebraicallySymmetry - algebraically
1.1.
2.2.
3.3.
3)( 2 xxf
22)( 2 xxxf
2
3
4)(
xxxf
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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)