Question

Sketch the graph of each rational function showing all the key features. Verify your graph by graphing the function on

the graphing calculator.
5. f(x) = x / x2 − 9

Answer 1

Rational Function

Explanation:

Gives the function:

`f(x) = (x)/(x^2-9)`

It has the following,

Domain

x∈
`\mathbb{R}` :
`x\\eq 3, x\\eq -3`

Range

`\mathbb{R}` (All real numbers)

End behaviour

As x
`x \rightarrow \infty, y \rightarrow 0`

Horizontal and Vertical Asymptote

Vertical
`x = 3, x=-3`

Horizontal
`y = 0`

x-intercept: (0,0)

y-intercept: (0,0)

**The Graph is in the annex