Vocab
What is a parent function?
The simplest of functions in a family.
g(x) = x + 11
Vertical translation 11 units up
g(x) = 5(x)
Vertical stretch by a factor of 5
g(x)=-(x)
g(x) = (x – 11) + 2
Horizontal translation 11 units right and Vertical translation 2 units up
What is a Transformation?
A transformation moves the graph on the coordinate plane, which can create new linear functions.
g(x) = x – 8
Vertical translation 8 units down
g(x) = 1.5(x)
Vertical stretch by a factor of 1.5
g(x)=(-x)
Reflection across the y axis
g(x) = 2(x – 6)
Vertical stretch by a factor of 2 and a translation 6 units right
What is a Translation
A translation is a transformation in which a figure is slid from one position to another without being turned.
g(x) = (x – 7)
Horizontal translation 7 units right
g(x) = (¾x)
Horizontal stretch by a factor of 4/3
g(x) = -4(x)
Vertical stretch by a factor of 4 and a reflection across the x-axis
g(x) = 3x – 5
Vertical stretch by a factor of 3 and a translation 5 units down
What is a Dilation?
A dilation stretches or compresses the graph of a function. When the graph of a linear function is dilated, its slope changes.
g(x) = (x + 12)
Horizontal translation 12 units left
g(x) =⅓(x)
Vertical compression by a factor of 1/3
g(x) = (-6x)
Horizontal compression by a factor of 1/6 and a reflection across the y-axis
g(x) = -4(x+6)
Vertical stretch by a factor of 4 and a reflection across the x-axis and a translation 6 units left
What is a reflection?
A reflection is a transformation in which a figure, line, or curve, is flipped across a line .
g(x) = (x + 10) – 1
Horizontal translation 10 units left and Vertical translation 1 unit down
g(x) = (0.4x)
Horizontal stretch by a factor of 5/2
g(x) = (-⅘ x)
Horizontal stretch by a factor of 5/4 and a reflection across the y-axis
g(x) = -(⅕x) + 4
Horizontal stretch by a factor of 5 and a reflection across the x-axis and a translation 4 units up