Today in Pre-Calculus
• Do NOT need a calculator• Go over homework• Notes: Non-Rigid Graphical
Transformations• Homework
Homework2) up 5.24) Right 36) Down 1008)Left 50 down 27910)Right 518)Reflect over x-axis, left 430)
Non-Rigid Transformations• Changes the size and shape of the graph.
• Types:
– Stretches
– Shrinks
– Can be vertical or horizontal
Vertical• Multiply equation by a factor c: y = c∙f(x)
• If c > 1, stretch by a factor of c
• If c < 1, shrink by a factor of c
y=x3-5x
y=2(x3-5x)
y=1/2(x3-5x)
Horizontal• Divide the x in the function by c:• If c > 1, stretch by a factor of c• If c < 1, shrink by a factor of c
y=x3-5x
y=(x/3)3-5(x/3)
y=(x/.5)3-5(x/.5)
xy f
c
Misc• Reflections: If c is negative in either the vertical
or horizontal stretch/shrink, the graph reflects and stretches/shrinks.
• Order matters when combining transformations1) Stretch/shrink
2) Reflections
3) Shifts
Example
Basic function: x2
Key points: (0,0), (1,1), (-1,1)
Vertical stretch 3 (multiply y by 3)
Down 4
2( ) 3 4f x x
Example
Basic function: x3
Key points: (0,0), (1,1), (-1,-1)
Reflect over x-axis
Vertical stretch 1/2 (multiply y by 1/2)
Right 3
31( ) 3
2f x x
Example
y = f(x – 2) + 3
b. y = 0.5f(x + 1) – 2 c.
0.5 1 2y f x
2 1 3y f x
Homework• Pg 147: 13-16, 21, 24, 26, 39, 43, 44, 47, 49, 51-
54(use handout)
• Memorize 10 basic functions
• Quiz Monday, September 29
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