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HRW Alg 2 Lesson 1.3.Notes2.notebook
1
September 10, 2015
Sep 98:24 AM
Aug 304:50 PM
Unit 1, Module 1
1.3 Transformations of Function Graphs
HRW Alg 2 Lesson 1.3.Notes2.notebook
2
September 10, 2015
Sep 12:21 PM
Translation: Shifts a function vertically and horizontally
Graph y1 = x2 Graph y2 = x2 + 3 What happened to the graph?
Graph y3 = x2 – 7 What happened to the graph?
Let f(x) be the parent function and let k > 0
Vertical shift k units up g(x) = f(x) _______
Vertical shift k units down g(x) = _____________
Graph y1 = x2 Graph y2 = (x+3)2 What happened to the graph?
Graph y3 = (x ‐ 7)2 What happened to the graph?
Let f(x) be the parent function and let h > 0 Horizontal shift h units right g(x) = _____________
Vertical shift h units left g(x) = _____________
Sep 22:03 PM
ex. Describe the translation to the parent function f(x) = √x, then graph.
a.) g(x) = √ x+ 7 ‐ 5
b.) g(x) = √x ‐ 3 + 4
ex. Write the new function give the translations to the parent function f(x) = x3
g(x) is translated 6 units up and 2 units left
HRW Alg 2 Lesson 1.3.Notes2.notebook
3
September 10, 2015
Sep 22:08 PM
Let f(x) be the parent function and let a > 1 Vertical stretch by a factor of a g(x) =________
Let f(x) be the parent function and let 0< a < 1
Vertical compression by a factor of a g(x) = _________
Vertical Stretch and Compression
* Does the domain or range of the function change after a vertical stretch or compression?
HRW Alg 2 Lesson 1.3.Notes2.notebook
4
September 10, 2015
Sep 22:08 PM
Let f(x) be the parent function and let b > 1 Horizontal compression by a factor of 1/b g(x) =________
Let f(x) be the parent function and let 0< b < 1
Horizontal stretch by a factor of 1/b g(x) = _________
Horizontal Stretch and Compression
* Does the domain or range of the function change after a horizontal stretch or compression?
HRW Alg 2 Lesson 1.3.Notes2.notebook
5
September 10, 2015
Sep 22:23 PM
ex. Describe the transformation to the parent function f(x) = √x
a.) g(x) = 5√ x
b.) g(x) = √2x
c.) g(x) = 1/3√ x
d.) g(x) = √ 1/4x
Sep 22:26 PM
Summary:
g(x) = a f(x + h) + k g(x) = f(b(x + h)) + k
ex. Graph the transformations to the following graph:
a.) Vertical stretch of 2 b.) Graph g(x) = f(1/2x)
f(x)
HRW Alg 2 Lesson 1.3.Notes2.notebook
6
September 10, 2015
Sep 22:30 PM
Reflections
Over the x‐axis: (x, y) ‐‐‐‐> ( ______ , _______)
f(x) = x2, g(x) = ‐x2
When a < 0 in g(x) = af(x), the function reflects over the x‐axis
Over the y‐axis: (x, y) ‐‐‐‐> ( ______ , _______)f(x) = x, g(x) = ‐xWhen b < 0 in g(x) = f(bx), the function reflects over the y‐axis
HRW Alg 2 Lesson 1.3.Notes2.notebook
7
September 10, 2015
Sep 22:33 PM
Use the graph to perform each transformation.
5. Transform y = k(x) by compressing it horizontally
by a factor of . Label the new function m(x).
Which coordinate is multiplied by ?
6. Transform y = k(x) by translating it down 3 units. Label the new function p(x). What happens to the ycoordinate in each new ordered pair?
7. Transform y = k(x) by stretching it vertically by a factor of 2. Label the new function q(x). Which coordinate is multiplied by 2?
8. Describe how the coordinates of a function change when the function is translated 2 units to the left and 4 units up.
HRW Alg 2 Lesson 1.3.Notes2.notebook
8
September 10, 2015
Aug 305:20 PM
HW 1.3 #1‐6, 10‐12, 15, 16
Just describe, no graph