3.2C   Increase/Decrease

Increasing, Decreasing, and Constant Functions

• The function y = x is a line and has a positive slope.
  Because the slope is positive, the function's graph is increasing on the interval from   -∞ to ∞.
  It is increasing on the interval from (-∞, ∞).

The function y = x2 is a parabola

• The vertex of this function is (0, 0)

• The left side has a negative slope, so from negative infinity to x = 0, the function is decreasing

• The right side has a positive slope, so, from x = 0 to positive infinity, the function is increasing

• This function is decreasing on the interval (-∞, 0) and increasing on the interval (0, ∞)

The function y = x3 is a cubic function

• This function has a positive slope from negative infinity to positive infinity,

  • so, it is increasing on the interval from (-∞, ∞)