Chapter 1 Function Transformationskillornmath.weebly.com/uploads/3/0/9/5/30958945/1.1... · 2019....
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1.1 Translations (Solutions).notebook September 10, 2015
Chapter 1
Function Transformations
What is a transformation?
A change made to a figure or relation such that the figure or the graph of the relation is shifted or changed in shape
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1.1 Translations (Solutions).notebook September 10, 2015
1.1
Translations
vertical translation (examples)
y = x2 + 7
y = x2 4
horizontal translation (examples)
y = (x 3)2
y = (x + 5)2
A translation is a horizontal or vertical "shift" that changes the position of the original function, but does not alter its size or shape.
For Example: If the quadratic function, y = x2, is moved horizontally or vertically from it's original location, its equation changes as well.
Always inside the bracket(ie. inside the function)
Always outside the bracket(ie. outside the function)
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1.1 Translations (Solutions).notebook September 10, 2015
1) Write the new function equation for each of the following after a translation of 4 units left and 9 units down.
y = x y = | x |
y = x2 y = x
y = x3 y = 1x
2) The original function and its translation are given on the grid below. State the equation of the translated function.
y = x2
a)
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1.1 Translations (Solutions).notebook September 10, 2015
f(x) = | x |
b)
y = 1
x
c)
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1.1 Translations (Solutions).notebook September 10, 2015
vertical translation (examples)
1) 7 up
2) 4 down
y = f(x)
horizontal translation (examples)
1) 5 right
2) 6 left
Translations can also be performed on the general function notation.
3) The original red function, y = f(x), and its blue translation are given. State the equation of the blue translated function.
y = f(x)
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1.1 Translations (Solutions).notebook September 10, 2015
Let's get ready to rumble!
Mathpower
Page 10:
#s 1 10, 1115(odd), 18, 21, 23, 28, 32(bdf), 33(bdf), 34(bdf)