4.7.2 Sketching the Graphs of Basic Polynomial Functions

Question 1

polynomial functions

Answer 1

• Graphs of polynomials with even degree have end behavior that is U-shaped. If the leading coefficient of the polynomial
  is positive, the U-shape is right side up. If the leading coefficient is negative, the U-shape is upside-down.
  • Graphs of polynomials with odd degree are S-shaped. If the leading coefficient of the polynomial is positive, the graph
  increases as x increases. If the leading coefficient is negative, then the graph decreases as x increases.
  • For the graphs of y = x^2, y = x^4, y = x^6, and so on, the higher the degree, the sharper the turns in the U-shape of the graph.
  • For the graphs of y = x, y = x^3, y = x^5 and so on, the higher the degree, the sharper the turns in the S-shape of the graph.