Question

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

the graphing calculator.
4. f(x) = x − 2 / 3x − 2x2

Answer 1

Rational Function

Explanation:

Gives the function:

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

It has the following,

Domain

x∈
`\mathbb{R}` :
`x\\eq 0, x\\eq 3/2`

Range

`f \in \mathbb{R} : f \leq -1, f \geq -(1)/(9)`

End behaviour

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

Horizontal and Vertical Asymptote

Vertical
`x = 0, x=3/2`

Horizontal
`y = 0`

x-intercept: (2,0)

y-intercept: none

**The Graph is in the annex