Question

The graph of a rational function f is shown below

Answer 1

From the given graph we get that the function has 2 vertical asymptotes x=-4 and x=2.

Also, from the graph, we get that the function has 1 horizontal asymptote y=0.

Now, notice that the points (0,1) and (-1,0) are on the graph, therefore the graph has only one x-intercept with coordinates (-1,0) and only one y-intercept with coordinates (0,1).

Since the graph has 2 vertical asymptotes at x=-4 and x=2, we get that its domain is:

`(-\infty,-4)\cup(-4,2)\cup(2,\infty).`

Finally, from the graph we get that the range of the function is:

`(-\infty,\infty)\text{.}`

Answer:

(a) Vertical asymptotes:

`x=-4\text{ and x=2.}`

Horizontal asymptotes:

`y=0.`

(b) x-intercepts 1.

y-intercepts 1.

(c) Domain:

`(-\infty,-4)\cup(-4,2)\cup(2,\infty).`

Range:

`(-\infty,\infty)\text{.}`