### Home > PC3 > Chapter 11 > Lesson 11.2.5 > Problem11-148

11-148.

Give $f(x) =\frac { 4 x - 5 } { 2 x - 3 }$.

1. Rewrite $f(x)$ in the form of $y = k +\frac { a } { 2 x - 3 }$.

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

2. State all of the asymptotes in the graph.

The vertical asymptote is the value of $x$ that causes division by $0$.
The horizontal asymptote is $y = k$.

3. Evaluate $\lim\limits_ { x \rightarrow - \infty } f ( x )$.

This is the horizontal asymptote.

4. Evaluate $\lim\limits_{ x \rightarrow 1.5 ^ { + } } f ( x )$.

Remember to approach $x = 1.5$ from the right.