Transformations Vocab
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a ___________ is a rigid transformation that has the affect of shifting the graph of a function up, down, left, or right
Translation
What does the transformation f(x)↦7f(x) do to the graph of f(x)?
Stretches it Vertically a = 7
What kind of transformation converts the graph of f(x) = -2x-5
into the graph of g(x) = -4x -10?
A vertical stretch by a factor of 2. a = 2
A linear function reflected across the x-axis, and vertically compressed by 1/2.
f(x)= -1/2x
Find the inverse of f(x)= -x
f-1(x)= -x
Which transformation of the graph of a linear function changes the direction of the graph?
Reflection
What does the transformation f(x)↦f(x-7) do to the graph of f(x)?
Horizontally translate the graph 7 units right.
h = 7
What kind of transformation converts the graph of f(x) = 9x-9
into the graph of g(x) = x -1?
Vertical Shrink by a factor of 1/9
Linear function moved left 18 units and translated down 2.
f(x) =( x + 18) - 2
Find the inverse of f(x)= 3x
f-1(x)= 1/3x
a ____________ of a parent function affects the location, size or shape of a parent graph
Transformation
What does the transformation f(x)↦f(x)-8 do to the graph of f(x)?
A vertical translation 8 units down.
K = -8
What kind of transformation converts the graph of f(x) = -x+8
into the graph of g(x) =x+8?
Reflection across the y-axis.
A linear function compressed vertically by 1/3, moved left 4 units.
f(x) = 1/3(x+4)
Find the inverse of g(x) = -5x+ 5
g-1(x) = -1/5x+1
what is it called when you enlarge OR shrink a graph proportionally?
Dilation
What does the transformation f(x)↦f(x - 10) - 4 do to the graph of f(x)?
~A horizontal translation 10 units right. h = 10
~A vertical translation 4 units down. k = -4
What kind of transformation converts the graph of f(x) = -2x+1
into the graph of g(x) = 2x -1?
Reflection across the x axis
A linear function reflected across the x-axis, stretched by 3, moved right 5 units and translated up 1 unit.
f(x) = -3(x-5) + 1
Find the inverse of h(x) =x -6
h-1(x)= x + 6
What do we call the "original" functions that are the root of all transformations?
Parent function
What does the transformation f(x)↦f(- 8x)+2 do to the graph of f(x)?
~A reflection across the y axis.
~A horizontal shrink by a factor of 1/8. a = 1/8
~A vertical translation 2 units up. k = 2
What kind of transformation converts the graph of f(x) = 4x-7
into the graph of g(x) = 4x-9?
Translate the graph 2 units down.
A linear function reflected across the y-axis, vertical stretch by 4, moved right 9, and up 11.
f(x) = 4(-x-9) +11
Find the inverse of h(x) = -3x - 8
h-1(x)= -1/3x - 8/3