Rules
What is the rule for vertical translation up?
g(x)=f(x)+k
What is the following parent function called?
f(x)=x
Linear
Describe the translation happening.
g(x)=-f(x-6)
Reflection across the x-axis, horizontally shift right 6 units.
The parent function of f(x)= 1/2 |x-9| is
f(x)= |x|
What is the rule for a horizontal stretch?
0<|a|<1
g(x)=f(1/c*x)
What is the rule for a vertical translation down?
g(x)=f(x)-k
What is the following parent function called?
f(x)=|x|
Absolute Value
Describe the translation happening.
g(x)=|1/3x|+9
Horizontal stretch by a factor of 1/3, vertical shift up by 9 units.
When reflecting something over the y-axis the negative sign goes
next to the x
What is the rule for horizontal compression?
(|a|>1)
g(x)=f(1/c*x)
What is the rule for a horizontal translation left?
g(x)=f(x+h)
What is the following parent function called?
f(x)=x2
Quadratic
Write an equation for the new function described below.
The graph of the absolute parent function is reflected across the y-axis, horizontally compressed by a factor of 5/3, and shifted down 2 units.
g(x)= |-5/3x|-2
A vertical stretch is when the number being multiplied by the function is
greater then 1
What is the rule for a vertical stretch?
|a|>1
g(x)=a*f(x)
What is the rule for a horizontal translation right?
g(x)=f(x-h)
What is the following parent function called?
f(x)=logx
Logarithmic
Write an equation for the new function described below.
The graph of a quadratic parent function is vertically stretched by a factor of 3 and shifted right 12 units.
g(x)= 3(x-12)2
When the function has a horizontal translation right the sign used to write the new function is a
minus sign
What is the rule for vertical compression?
0<|a|<1
g(x)=a*f(x)
What is the rule for a reflection across the y-axis?
g(x)=f(-x)
What is the following parent function called?
f(x)=x3
What is the parent function of the changed function below?
f(x)= 2(x-5)+9
Linear
A horizontal compression is when the number multiplied by the function is
greater then 1
What is the rule for a reflection across the x-axis?
g(x)=-f(x)