Definitions
x1 less than x2 and f(x1) is less than f(x2)
The graph is decreasing
even or odd (graph)
f(x)=x3+x
odd function
Continous
f(x)=x^3+3x/x even or odd (using -x)
even
f(-x)=f(x)
symmetry with respect to the y-axis
Find the equation that defines the function and determine the largest interval where the function is increasing and decreasing
y=(x+4)2+3
(-4, infinity) increasing
(-infinity, -4) decreasing
(a,b) is on the graph and so is (-a,-b)
symmetry with respect to the origin
Shift this function vertically 5 down and to the left 3
f(x)=[x], what is the new domain
show work on board
(a,b) is on the graph and so is (a,-b)
symmetry with respect to the x-axis
The function is increasing or decreasing over the interval (-infinity, infinity)
y=x5
increases