M3U1L02 Transformation of Functions .notebook
August 31, 2016
Math 3, U1, L02, Transformation of Functions
Be able to:
• Describe transformations that happen to functions based on their parent functions.
• Write functions given transformations and a parent function.
Know:
The transformation
notation of Learning Resources
Regents Exam Prep Center: Transformations with Functions
Read the first two lessons Hotmath.com: Exploring Transformations
Khan Academy: Algebra: Graphs of Square Root Functions Visual Calculus: Transformation of Functions
M3U1L02 Transformation of Functions .notebook
August 31, 2016
a : Vertical Stretch by a factor of |a|.
a < 0 : Reflected about the x­axis i.e. "flipped vertically"
b : Horizontal Compression by a factor of |1/b|.
d : Vertical Shift
­c/b : Horizontal shift
b < 0 : Reflected about the y axis i.e. "flipped horizontally" Go to this graphing tool before moving on https://www.desmos.com/calculator
to the next slide
In Desmos...
Set line #1 to: y=x^3
Set line #2 to: y=a(bx+c)^3+d
Establish sliders for a through d on lines three through six.
Set a = 1, b = 1, c = 0 and d = 0 using their sliders.
M3U1L02 Transformation of Functions .notebook
August 31, 2016
y=a(bx+c)3+d
Determine each equation for translating y = x3:
Stretch vertically by a factor of two
y = ­(x)3
y = 2(x)3
Compress horizontally by a factor of 1/2 y = (2x)3
Shift vertically up 4 units
y = (x)3 + 4
Shift horizontally left 5 units
y = (x + 5)3
Flip horizontally
y = (­x)3
Flip vertically
Shift down two, right 5 and stretch horizontally by a factor of two.
Hint: Horiz. Shift = ­c/b
y = (0.5x ­ 2.5)3 ­ 2
y=a*sqrt(bx+c)+d
Determine each equation for translating y = sqrt(x):
Stretch vertically by a factor of two
y = ­sqrt(x)
y = 2sqrt(x)
Compress horizontally by a factor of 1/2 y = sqrt(2x)
Flip vertically
Shift vertically up 4 units
y = sqrt(x) + 4
Shift horizontally left 5 units
y = sqrt(x + 5)
Flip horizontally
Shift down two, right 5 and stretch horizontally by a factor of two.
y = sqrt(­x)
Hint: Horiz. Shift = ­c/b
y = sqrt(0.5x ­ 2.5) ­ 2
M3U1L02 Transformation of Functions .notebook
August 31, 2016
y=a*2(bx+c)+d
Determine each equation for translating y = 2(x):
Stretch vertically by a factor of three
y = ­2(x)
y = 3*2(x)
Compress horizontally by a factor of 1/3 y = 2(3x)
Flip vertically
Shift vertically up 4 units
y = 2(x) + 4
Shift horizontally left 5 units
y = 2(x + 5)
y = 2(­x)
Flip horizontally
Shift down two, right 5 and stretch horizontally by a factor of two.
Hint: Horiz. Shift = ­c/b
y = 2(0.5x ­ 2.5) ­ 2
What is the simplified equation in standard form for the translation of: 3 2 y = x ­ 2x ­ 15x
if it is moved four units left and 3 units up?
y = x3 + 10x2 + 17x ­ 25
M3U1L02 Transformation of Functions .notebook
August 31, 2016
Math 3 U1 L02 Homework
Regents Exam Prep Center: Transformations with Functions
Do the Practice.
Braingenie: Determining The Correct Translation Given Two Graphs Braingenie: Determine the correct Graph given the translation
Braingenie: Graphing Verticle and Horizontal Shift
Braingenie: Graphing Vertical and Horizontal Stretches
Braingenie: Parent Functions and Transformations: Multiplayer game.