Question

Answer parts a through E for the function shown below.What would the x intercepts be?

Answer 1

We have the following function:

`f(x)=x^3-6x^2`

The leading coefficient is the number written in front of the variable with largest exponent. In our case, the largest exponen is 3 (which is an odd number), so the leading coefficient is 1.

Then, since the degree is odd (3) and the leading coefficient is positive, the graphs falls on left and rises right. By comparing with the given options, the answer is A.

The x-intercept ocurrs when y=0. So we need to solve the following equation:

`x^3-6x^2=0`

which can be rewritten as

`x^2(x-6)=0`

This give us 2 solutions:

`\begin{gathered} x=0 \\ \text{and} \\ x=6 \end{gathered}`

Therefore, the x-intercetps ocurr at x=0 and x=6.