The question gives us the following function:
[tex]f(x)=\frac{3x}{x-2}[/tex]
The X-intercept is where the function crosses the x-axis and the Y-intercept is where the function crosses the y-axis.
X-intercept:
Since the graph must cross the x-axis to have an x-intercept, we should equate f(x) to zero.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2}=0 \\ \\ 3x=0 \\ \therefore x=0\text{ is the x-intercept} \end{gathered}[/tex]
Y-intercept:
Since the graph must cross the y-axis to have a y-intercept, we should equate x = 0.
[tex]\begin{gathered} f(x)=\frac{3x}{x-2} \\ \\ f(0)=\frac{3(0)}{0-2} \\ \\ f(0)=0\text{ is a y-intercept} \end{gathered}[/tex]
Answer
Thus, the x and y-intercepts are: x = 0 and y = 0 respectively
