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

Answer:

Rational Function

Step-by-step explanation:

Gives the function:

$f(x) = \frac{x-2}{3x-2x^2}$

It has the following,

Domain

x∈ $\mathbb{R}$ : $x\neq 0, x\neq 3/2$

Range

$f \in \mathbb{R} : f \leq -1, f \geq -\frac{1}{9}$

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