Download 3.6 Transformations of Functions II

Algebra 2/Trigonometry 3
Name: ____________________________
Transformations of Functions II
Notes Sheet
Learning
Goals:
At the completion of the lesson, you will be able to…
1) Write the equations of shifted Parent Graphs
Function
Constant Function
Identity Function
Parent Function
f ( x)  c
f ( x)  x
General Equation Form
f ( x)  c  B
f ( x)  A( x  B)  C
Example
f ( x)  2  5
f ( x)  12 ( x  4)  6
Quadratic Function
f ( x)  x 2
f ( x)  A( x  B) 2  C
f ( x)  3( x  7) 2  8
Cubic Function
f ( x)  x 3
f ( x)  A( x  B) 3  C
f ( x)  34 ( x  1) 3  9
Square Root Function
f ( x)  x
f ( x) | x |
f ( x)  A x  B  C
f ( x )  A | x  B | C
f ( x)  1 x  5  2
f ( x)  8 | x  2 | 1
1
x
 1 
f ( x)  A
C
xB
 1 
f ( x)   14 
3
 x 6
Absolute Value Function
Reciprocal Function
f ( x) 
Transformations (A)
Whole
Negative
Negative Fraction
Number x-variable
Vertical
Vertical Vertical Horizontal
Reflection Shrink
Stretch Reflection
Horizontal Shifts (B)
Vertical Shifts (C)
Negative
Zero
Positive
Negative
Zero
Positive
Shift
Right
No Effect
Shift
Left
Shift
Down
No Effect
Shift Up
In order to create the function that a graph represents:
***
1) Identify the Parent Function by the shape of the graph.
2) The coordinates of the vertex are (-B, C) so you can use
these values to find the values of B and C.
3) Plug the values of B and C into the general equation of
your parent function.
4) To determine the numerical value of A, pick any point
(other than the vertex) from the graph and plug these
coordinates in for x and y in the general equation of the
parent function. Solve for A.
***Do an example of a square root graph that
is y-axis flipped***
f ( x)   ( x  3)  5