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Unit 2: FunctionsUnit 2: Functions
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:  T...
TranslationsTranslations
 First, you have to know what the parentFirst, you have to know what the parent
functions look l...
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!
...
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 f...
GraphGraph
 Exponential ExampleExponential Example  Log ExampleLog Example
1
2 5x
y −
= + log( 5) 1y x= − +
Practice GraphingPractice Graphing
 2 1y x= − + − ( )
3
3 1y x= − − − +
SymmetrySymmetry
Symmetry - ExamplesSymmetry - Examples
 w/ respect to the y-axisw/ respect to the y-axis (EVEN)(EVEN)
 f(x) = xf(x) = x2...
Symmetry -Symmetry -
algebraicallyalgebraically
1.1.
2.2.
3.3.
3)( 2
−= xxf
22)( 2
−−= xxxf
2
3
4
)(
x
x
xf
−
=
HomeworkHomework
 P. 99 (47-54, 63-66P. 99 (47-54, 63-66 state endstate end
behavior using limits toobehavior using limit...
Functions worked
Functions worked
Functions worked
Functions worked
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Functions worked

  1. 1. Unit 2: FunctionsUnit 2: Functions
  2. 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. 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…
  4. 4. 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= − − +
  5. 5. 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)
  6. 6. GraphGraph  Exponential ExampleExponential Example  Log ExampleLog Example 1 2 5x y − = + log( 5) 1y x= − +
  7. 7. Practice GraphingPractice Graphing  2 1y x= − + − ( ) 3 3 1y x= − − − +
  8. 8. SymmetrySymmetry
  9. 9. 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
  10. 10. Symmetry -Symmetry - algebraicallyalgebraically 1.1. 2.2. 3.3. 3)( 2 −= xxf 22)( 2 −−= xxxf 2 3 4 )( x x xf − =
  11. 11. 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)

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