math help!?

Question

For eqn: 1/x^2
- what is the range?
-symmetry of graph?
-intervals of increasing or decreasing
-any local max or min

Answer 1

Range: x>0
Symmetry: About the origin, x = 0
Intervals: Increasing: x < 0
Decreasing: x > 0
Local min: x = 0
Local max: none, diverges as x => (goes to) 0

1/0 is undefined, so y approaches infinity as x gets smaller and smaller.

Answer 2

To find the range of the eqn, just specify all possible y-values.

For symmetry you can do it by logic or by math. Doing it by math means that you have to input (x,-y) for x axis, (-x,y) for y axis, switch the x and y for the line y=x, and (-x,-y) for origin symmetry and check if the new and original equation are the same.

For intervals of increasing and decreasing it is easiest to graph and check where the graph goes from upper left to lower right for decreasing and vice versa for increasing.

There are no local min/max for this eqn, it grows infinitely larger and smaller.

Answer 3

Well, x cannot be zero, but as x increases, then f(x) becomes smaller, so
range: (-infinity,0), (0,infinity)
symmetry: about the vertical axis at x=0
intervals: increasing (-infinity,0), decreasing (0,infinity)
local: none