Question

select the x - intercept(s) and y - intercept of the function, if one exists. f(x)=\frac{x^{2}-9}{x + 4} x - ints: (3, 0) and (-3, 0) y - ints: (3, 0) and (-3, 0) y - int: (0, -\frac{9}{4}) x - int: none x - int: (0, -\frac{9}{4})

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$, so $\frac{x^{2}-9}{x + 4}=0$. Since a fraction is 0 when the numerator is 0 and the denominator is non - zero. Set $x^{2}-9 = 0$, which factors to $(x + 3)(x - 3)=0$. Solving gives $x=3$ or $x=-3$, and for both values $x+4
eq0$.

Step2: Find y - intercept

Set $x = 0$ in $f(x)$. Then $f(0)=\frac{0^{2}-9}{0 + 4}=-\frac{9}{4}$. The y - intercept is the point $(0,-\frac{9}{4})$.

Answer:

x - ints: (3, 0) and (-3, 0)
y - int: $(0,-\frac{9}{4})$