Home > PC3 > Chapter 7 > Lesson 7.2.5 > Problem7-128

7-128.

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

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

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

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.