1.1 Parent Functions and Transformations Flashcards
Function Notation
A way to write a function when one variable is expressed in terms of another
Parent Functions
The most basic function in a family
Constant
f(x)=1
Linear
g(x)=x
Absolute Value
h(x)= IxI
v shaped graph
Quadratic
k(x)=x^2
U shaped graph
Transformation
Changes the size, shape, position or orientation of a parent function
Translation
A transformation that shifts a graph vertically and/or horizontally, but does not change its shape or size
Changes from parent function:
Number added/subtracted to input INSIDE grouping
- Moves right/left-affects the x value
- Goes in opposite direction than you would expect based on +/-
Changes from parent function:
Number added/subtracted to input OUTSIDE grouping
- Moves up/down-affects y value
- Goes in direction you wou;d expect based on +/-
Vertical Stretches and Shrinks
widens or narrows the graph
Changes from parent function:
When the factor is greater than 1
- Grpah stretches vertically=narrrow
- Increases faster
Changes from parent function:
When factor is between 0 and 1
- Graph shrinks vertically=wider
- Increases slower
Reflections
a transformation that flips a graph over a line called the line of reflection
Changes from the Parent Function
Negative of the parent function
Reflects the graph over the x axis