Section 2.5 Transformations of Functions Vertical Shifting EXAMPLE: Use the graph of f (x)= x 2 to sketch the graph of each function. (a) g(x)= x 2 +3 (b) h(x)= x 2 − 2 EXAMPLE: Use the graph of f (x)= x 3 − 9x to sketch the graph of each function. (a) g(x)= x 3 − 9x + 10 (b) h(x)= x 3 − 9x − 20 1
10
Embed
Section 2.5 Transformations of Functionsteacherpress.ocps.net/.../Transformations-of-Functions.pdf · 2020. 2. 26. · Section 2.5 Transformations of Functions Vertical Shifting EXAMPLE:
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Section 2.5 Transformations of Functions
Vertical Shifting
EXAMPLE: Use the graph of f(x) = x2 to sketch the graph of each function.
(a) g(x) = x2 + 3 (b) h(x) = x2 − 2
EXAMPLE: Use the graph of f(x) = x3 − 9x to sketch the graph of each function.
(a) g(x) = x3 − 9x+ 10 (b) h(x) = x3 − 9x− 20
1
EXAMPLE: Use the graph of f(x) = x3 − 9x to sketch the graph of each function.
(a) g(x) = x3 − 9x+ 10 (b) h(x) = x3 − 9x− 20
Horizontal Shifting
EXAMPLE: Use the graph of f(x) = x2 to sketch the graph of each function.
(a) g(x) = (x+ 4)2 (b) h(x) = (x− 2)2
2
EXAMPLE: Use the graph of f(x) = x2 to sketch the graph of each function.
(a) g(x) = (x+ 4)2 (b) h(x) = (x− 2)2
EXAMPLE: How is the graph of y = f(x− 3) + 2 obtained from the graph of f?
Answer: The graph shifts right 3 units, then shifts upward 2 units.
EXAMPLE: Sketch the graph of f(x) =√x− 3 + 4.
Reflecting Graphs
EXAMPLE: Sketch the graph of each function.
(a) f(x) = −x2 (b) g(x) =√−x
3
EXAMPLE: Sketch the graph of each function.
(a) f(x) = −x2 (b) g(x) =√−x
EXAMPLE: Given the graph of f(x) =√x, use transformations to graph f(x) = 1−