Question

Find the range of the function Find the x and y intercepts

Answer 1

For the function f(x) to be greater than 0 (f(x) > 0), we need to identify those regions strictly above the x-axis.

From the graph, these regions are (in interval notation):

`\begin{gathered} R_1=(-6,-1) \\ \\ R_2=(4,6\rbrack \end{gathered}`

For each region there is an inequality:

`\begin{gathered} R_1:-6\lt x\lt-1 \\ \\ R_2:4\lt x\leqslant6 \end{gathered}`

The domain is the set of x-values the function takes. Then, from the graph, we can see that the function is defined from x = -7 to x = 6. The domain of f(x) is:

`Dom_f={}\lbrace x|-7\leqslant x\leqslant6\rbrace`

The range is the set of y-values the function takes. From the graph, we see that the function has a minimum of -8 and a maximum of 12. Then, the range is:

`Ran_f={}\lbrace y|-8\leqslant y\leqslant12\rbrace`

For the x-intercepts (points with y = 0), we have:

`-6,-1,4`

For the y-intercept (the point with x = 0):

`-4`