Sketching Graphs of Polynomials Help

Introduction Sketching Graphs of Polynomials

To sketch the graph of most polynomial functions accurately, we need to use calculus (don’t let that scare you—the calculus part is easier than the algebra part!) We can still get a pretty good graph using algebra alone. The general method is to plot x -intercepts (if there are any), a point to the left of the smallest x -intercept, a point between any two x -intercepts, and a point to the right of the largest x -intercept. Because y -intercepts are easy to find, it wouldn’t hurt to plot these, too.

Examples

Sketching Graphs of Polynomials Practice Problems

Practice

Match the graph of the given function with one of the graphs in Figures 7.1-7.4.

1. f(x) = −8 x ³ + 4 x ² − 9 x + 3
2. f(x) = 4 x ⁵ + 10 x ⁴ − 3 x ³ + x ²
3. P(x) = − x ² + x − 6
4. g(x) = 1 + x + x ² + x ³

Identify the x -intercepts and factors for the polynomial function whose graphs are given.

5.  

   

   Fig. 7.9

6.  

    

   

   Fig. 7.10

7.  

    

   

   Fig. 7.11

Match the polynomial function with one of the graphs in Figures 7.9 through 7.11 .

Solutions

Practice problems for this concept can be found at: Polynomial Functions Practice Test.