You now have enough information to sketch polynomial functions without the use of technology.

In this lesson you have been given the factored form of polynomials of degree 3 or higher. In the next lessons you will look at how to factor polynomials of degree 3 or higher.

Here is an outline of the steps to use:

Step 1: Determine the end behaviour by looking at the degree of the polynomial and the sign of the leading coefficient.

Step 2: Factor the polynomial if it is not given in the problem.

Step 3: Determine the x-intercepts by looking at the factors of the polynomial.

Step 4: Determine the y-intercept by substituting zero into the function.

Step 5: Determine the nature of the x-intercepts (whether there is a sign change) by looking at the multiplicity of the polynomial’s factors.

Step 6: Draw a smooth curve through the x- and y-intercepts.

Watch Sketching Polynomial Functions to see an example of graphing a function without using technology.

Self-Check 4

1. For each of the following functions, factor the function and create a sketch without technology.
   1. f(x) = x2 − x − 6 Answer
   2. f(x) = −x2 + 7x − 10 Answer
2. For each of the following functions, create a sketch without technology.
   1. f(x) = (x + 3)(x − 2)(x + 1) Answer
   2. f(x) = (x + 3)2(x − 2) Answer
   3. f(x) = −(x + 3)3(x − 4) Answer
   4. f(x) = (x − 2)(x + 2)(x − 1)(x + 1)(x − 3) Answer