Power and Polynomial Functions: Background You’ll Need 3

  • Identify the key features of quadratic and cubic functions

Quadratic Function: [latex]y = x^2[/latex]Graph of a parabola.

  • Domain and Range
    • Domain: All real numbers [latex](-\infty, \infty)[/latex]
    • Range: [latex][0, \infty)[/latex]
  • Behavior:
    • The function is increasing on [latex](0, \infty)[/latex]
    • The function is decreasing on [latex](-\infty, 0)[/latex]
  • Key Features: The minimum is [latex]y = 0[/latex], which occurs at [latex]x=0[/latex]. This minimum point of the parabola is called a vertex.

Cubic Function: [latex]y = x^3[/latex]Graph of f(x) = x^3.

  • Domain and Range
    • Domain: All real numbers [latex](-\infty, \infty)[/latex]
    • Range: All real numbers [latex](-\infty, \infty)[/latex]
  • Behavior:  The function is increasing on [latex](-\infty, \infty)[/latex]