Sketching the Graphs of Basic Polynomial Functions (4.7.2)

Question 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.

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.

Question 2

• 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.

Answer 2

• 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.

Question 3

• 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.

Answer 3

• 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.

Question 4

• 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.

Answer 4

• 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.