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Functions (Properties of Functions (Function vs. Relation (Function…
Functions
Properties of Functions
Domain (Independent Variable)
All X-values that satisfy a function
Range (Dependent Variable)
All Y-values of a function that come out of the X-input
Vertical Line Test
Determines if a line is a function
Zeros
X-intercepts
Function vs. Relation
Function implies for every x there is exactly one y
Relation does not imply the same
Reflections and Symmetry
Reflection over Y-Axis
(x,y) ---> (-x,y)
Reflection over X-Axis
(x,y) ---> (x,-y)
Reflection over Origin
(x,y) ---> (-x,-y)
Reflection over the line y=x
(x,y) ---> (y,x)
Symmetry over Y-Axis
Vertical Line Test
Periodic Functions, Stretching, and Translating Graphs
Translations
Period
How often a certain pattern repeats
Stretches
Vertical Stretch/Shrink
Horizontal Stretch/Shrink
Amplitude
Y-max - Y-min / 2
Reflections
Goes over a specific line/point
Operations on Functions
Difference
Product
Sum
Quotient
Inverse Functions
Horizontal Line Test
Determines if the inverse of the function is a function
Reflections over the line y=x