Parent Functions

• Linear Function: y = x


  Domain (-∞, ∞) Range (-∞,∞)

  • f(x) = x is increasing on its entire domain, (-∞, ∞).
  • It is continuous on its entire domain, (-∞, ∞).

  
• Quadratic Function: y = x²

  Domain (-∞, ∞) Range [0, ∞)

  The graph is a parabola. The point at which the graph changes from decreasing to increasing or increasing to decreasing is the vertex.

  • f(x) = x² decreases on the open interval (-∞,0) and increases on the open interval, (0,∞).
  • It is continuous on its entire domain, (-∞, ∞).
• Cubic Function: y = x³


  Domain (-∞, ∞) Range (-∞, ∞)

  The point (0,0) at which the graph changes from "opening downward" to "opening upward" is an inflection point.

  • f(x) = x³ increases on its entire domain, (-∞, ∞).
  • It is continuous on its entire domain, (-∞, ∞).

  
• Absolute Value Function: y = |x|


  Domain (-∞, ∞) Range [0, ∞)

  • f(x) = |x| decreases on the open interval (-∞, 0) and increases on the open interval (0, ∞).
  • It is continuous on its entire domain, (-∞, ∞).