Absolute+Values

The absolute value brackets basically makes everything positive. ex. |3| = 3
 * -3| =3

The absolute value functions "y = |x|" looks something like this:

ex. |x| < 8 -8 < x < 8
 * Absolute values and inequalities:**
 * x| ≥ 3 x ≤ -3 or x ≥ 3

y = |x-d| is shifted "d" units to the right y = |x| + c is shifted "c" units up
 * Translations of y = |x|**

ex. y = |x+2| is shifted 2 units to the left. y = |x| - 3 is shifted 3 units down

__**Properties of Functions**__

Intervals of increase and decrease:

Intervals of increase: the intervals in the function's domain where the y-values of the function get larger as you move from left to right.

Intervals of decrease: the intervals in the function's domain where the y-values of the function get smaller as you move from left to right.

Discontinuities: a break in the graph. ex. vertical asymptotes, jumps, holes, etc.

Symmetry: even, odd, neither

__Odd__ functions have rotational symmetry. Rotating the graph 180 degrees produces the same graph. f(-x) = -f(x) ex. y = x^3

__Even__ functions can be reflected across the y-axis and do not change. f(x) = f(-x) ex. y = x^4

End behaviour: How the function behaves as x approaches infinity and negative infinity. ex. for y = 1/x as x --> infinity, y --> 0