Transformations Powerpoint

1. By: Ms. Ball

2.  Take a moment and quietly discuss with a
neighbor, what are some parent functions
that you remember from earlier in this unit?
 Do you recall the nameAND the equation?

4.  Now that we remember some of our parent
functions, we can start to manipulate, or
transform them!
 Definition:
 The graph of a function is transformed when its
parent function is changed.
 There are three (3) types of transformations:
1. Shifts
2. Reflections
3. Stretches and Compressions

5.  Definition:
 When a graph is shifted it moves either up, down,
left, or right.
 Think about the x-y coordinate plane.Which
axis goes from left to right?What about up
and down?

6.  When an image is reflected, it is flipped like a
mirror
 There are 2 main reflections:
 About (across) the x-axis
 About the y-axis

7.  The coefficients of a function determine how
much it is stretched or compressed
 Given y = f(x),
 Horizontal stretching/compression will give you
y = f(ax), where “a” is a constant
 Vertical stretching/compression will give you
y = a f(x), again “a” is a constant

8.  A horizontal stretching
moves the graph away from
the y-axis
 A horizontal compression
squeezes the graph toward
the y-axis
 In changing a function from
f(x) to f(ax),
▪ If 0<a<1, its is stretched
horizontally by “a” units
▪ If a>1, the graph is compressed
horizontally by “a” units

9.  A vertical stretching
moves the graph away
from the x-axis
 A vertical compression
squeezes the graph
toward the x-axis
 In changing a function from
f(x) to f(ax),
▪ If 0<a<1, its is compressed
vertically by “a” units
▪ If a>1, the graph is stretched
vertically by “a” units

10.  Here’s a short video to go over what we just learned…
https://www.youtube.com/watch?v=7S5HF38DnUY

11.  Using the quadratic as your parent function,
write the equations of the given
transformations:
 Shifted 5 units up
 Shifted 3 units left, and stretched horizontally by
2
 Reflected across the y-axis, and shifted up 4