Functions & Transformations
What is the parent function for a linear function?
y=x
What is the parent function for a quadratic function?
y=x^2
What is the parent function for a square root function?
y=sqrt(x)
What is the parent function for a reciprocal function?
y=1/x
What is the parent function for an absolute value function?
y=|x|
What is the basic representation of a transformed function?
y=af(k(x-d))+c
What is the rule that makes a something a function?
1 input correlates to only 1 output / vertical line test
What does "a" do in transformations?
vertical stretch & compression, reflection along the x-axis
What does "k" do in transformations?
Horizontal stretch & compression, reflection along the y-axis
What does "c" do in transformations?
Translates a function on the y-axis
What does "d" do in transformations?
Translates a function on the x-axis
What does vertical stretching do to a function?
skinny
What does vertical compression do to a function?
wide
What does horizontal compression do to a function?
skinny
What does horizontal stretching do to a function?
wide
If a = 5, what happens to a function?
vertical stretching (skinny)
If a = 0.5, what happens to a function?
Vertical compression (wide)
If a = 1, what happens to a function?
Nothing
If a = -5, what happens to a function
Reflection on the x-axis, vertical stretching (skinny)
If a = -0.5, what happens to a function?
Reflection on the x-axis, vertical compression (wide)
If a = -1, what happens to a function?
Reflection on the x-axis
If k=5, what happens to a function?
Horizontal compression (skinny)
If k=0.5, what happens to a function?
Horizontal stretching (wide)
If k=1, what happens to a function?
Nothing
If k=-1, what happens to a function?
Reflection on the y-axis
If k=-5, what happens to a function?
Reflection on the y-axis, horizontal compression (vertical)
If k=-0.5, what happens to a function?
Reflection on the y-axis, Horizontal stretching (wide)
Does 'domain' refer to the x or y axis?
x-axis
Does 'range' refer to the x or y axis?
y-axis
If c = 5, what happens to a function?
Translated up by a factor of 5
if c=0.5, what happens to a function?
Translated up by a factor of 0.5
If c = 0, what happens to a function?
Nothing
If c=-5, what happens to a function?
Translated down by a factor of -5
If c=-0.5, what happens to a function?
Translated down by a factor of -0.5
If c=1, what happens to a function?
Translated up by a factor of 1
If d is shown as 5 in an equation, what happens to a function?
Translated left by a factor of -5
If d is shown as -5 in an equation, what happens to a function?
Translated right by a factor of 5
If d is shown as 0.5 in an equation, what happens to a function?
Translated left by a factor of -0.5
If d is shown as -0.5 in an equation, what happens to a function?
Translated right by a factor of 0.5
If d is shown as 0 in an equation, what happens to a function?
Nothing
If d is shown as 1 in an equation, what happens to a function?
Translated left by a factor of -1