Question

Describe the graph of the function at its roots. g(x) = (x + 4)4(x − 9) At x = −4, the graph the x–axis. At x = 9, the graph the x–axis.

Answer 1

At x = −4, the graph touches the x–axis. At x = 9, the graph crosses the x–axis.

Describing the graph of the function at its roots.

From the question, we have the following parameters that can be used in our computation:

g(x) = (x + 4)⁴(x − 9)

The roots of the above function are

x = -4 and x = 9

However, at these roots; The multiplicities are

x = -4; multiplicity = 4

x = 9; multiplicity = 1

This means that

The graph turns at x = -4 and crosses the x-axis at x = 9