Answer
The graph is shown below:
Work Step by Step
To find the x-intercepts of the function, equate the function $f\left( x \right)=\frac{\left( x-1 \right)}{\left( x-2 \right)}$ to zero.
$\begin{align}
& \frac{\left( x-1 \right)}{\left( x-2 \right)}=0 \\
& x=1
\end{align}$
Thus, $x=1$ is the x-intercept.
Equate the denominator to zero for the vertical asymptote:
$\left( x-2 \right)=0$
The vertical asymptote is $x=2$.
Compare the degrees of the numerator and denominator to find the horizontal asymptote. Since the degree of the numerator and denominator is 1, so the horizontal asymptote is $y=1$.
To find the y-intercept of the function, find the value of $f\left( 0 \right)$.
$\begin{align}
& f\left( 0 \right)=\frac{\left( 0-1 \right)}{\left( 0-2 \right)} \\
& =\frac{1}{2}
\end{align}$
Thus, the y-intercept is $\frac{1}{2}$.
Substitute x with $-x$ to check the symmetry of the function:
$\begin{align}
& f\left( -x \right)=\frac{\left( -x-1 \right)}{\left( -x-2 \right)} \\
& =\frac{\left( x+1 \right)}{\left( x+2 \right)}
\end{align}$
Since $f\left( x \right)\ne f\left( -x \right)$, the graph is not symmetric with respect to the y-axis and since $f\left( -x \right)\ne -f\left( x \right)$, the graph is not symmetric through the origin.
