Possible input values. X.
Possible output values. Y.
f(x) = f(-x)
f(x) = -f(x)
Every output happens exactly once.
[f(x+h) - f(x)] / h
Swap x and y then solve.
One-to-One Functions (Graph)
Each horizontal line crosses the line exactly once.
Onto Function (Graph)
Each horizontal line crosses the line at least once.
The function hits all possible y's.
Vertex of Parabola
x = [-b] / [2a]
Parabola opens up
When A is positive
Parabola opens down
When A is negative
Let all x's equal 0.
Set equation equal to 0 then factor.
Shirt Graph Right
Replace x with (x - a). Where a is constant.
Shift Graph Left
Replace x with (x + a). Where a is constant.
Shift Graph Up Vertically
Add a to f(x). (ie f(x) +3). Where a is constant.
Shift Graph Down Vertically
Subtract a from f(x). (ie f(x) -3). Where a is constant.
Flip over X-Axis
Replace f(x) with -f(x).
Flip over Y-Axis
Replace f(x) with f(-x)
Compress Graph Horizontally
Multiply x by constant a. (ie f(ax)). Where a is a cosntant.
Stretch Graph Horizontally
Multiply x by constant 1/a. (ie f((1/a)x)). Where a is a cosntant.
Compress Graph Vertically
Multiply f(x) by constant 1/a. (ie (1/a)f(x)). Where a is a constant
Stretch Graph Vertically
Multiply f(x) by constant a. (ie (a)f(x)). Where a is a cosntant.
None: Highest power is in numerator.
y=0: Highest power in in denominator only.
Fraction: Both numerator and denominator have same highest power.
Where denominator is equal to 0.
Numerator is a power 1 higher then the denominator.
Divide equations. Ignore remainder.