Question

determine the x and y intercepts of the following rational function f(x) = \frac{x^{2}-6x}{x^{2}-36}

x - int: (-6,0)
y - int: (0,0)

x - int: (0,0)
y - int: (0,0)

x - int: (-6,0) and (6,0)
y - int: (0,0)

x - int: none
y - int: (0,0)

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$, so $\frac{x^{2}-6x}{x^{2}-36}=0$. Since a fraction is 0 when the numerator is 0 and the denominator is not 0. Solve $x^{2}-6x = 0$. Factor out $x$: $x(x - 6)=0$. So $x=0$ or $x = 6$. When $x = 6$, the denominator $x^{2}-36=6^{2}-36=0$, so $x = 6$ is not an x - intercept. When $x=0$, the denominator $0^{2}-36=-36
eq0$. So the x - intercept is $(0,0)$.

Step2: Find y - intercepts

Set $x = 0$ in $f(x)$. Then $f(0)=\frac{0^{2}-6\times0}{0^{2}-36}=\frac{0}{-36}=0$. So the y - intercept is $(0,0)$.

Answer:

x - int: $(0,0)$
y - int: $(0,0)$