Answer
The graph is shown below:
Work Step by Step
Consider the functions, $f\left( x \right)=\frac{{{x}^{2}}-4x+3}{x-2}$ and $g\left( x \right)=\frac{{{x}^{2}}-5x+6}{x-2}$.
The graph of the functions $f\left( x \right)=\frac{{{x}^{2}}-4x+3}{x-2}$ and $g\left( x \right)=\frac{{{x}^{2}}-5x+6}{x-2}$ can be plotted using the TI-83 in the steps given below:
Step 1: Write the function ${{Y}_{1}}=\frac{{{x}^{2}}-4x+3}{x-2}$ and ${{Y}_{2}}=\frac{{{x}^{2}}-5x+6}{x-2}$.
Step 2: After that, set the window from $\left( -5,5,1 \right)$ on the $x$ -axis and $\left( -5,5,1 \right)$ on the $y$ -axis.
Step 3: Then, press TRACE.
As can be observed from the above graph that the function $f$ is symmetric about the line $x=2$. And, it has a vertical asymptote at $x=2$ , a slant asymptote at $x-2=0$ , and no horizontal asymptote.
Also, the graph $g$ is a straight line and passes through the points $\left( 0,-3 \right)$ and $\left( 0,3 \right)$. And, the graph $g$ has no vertical and horizontal asymptote.
