Question

determine the x and y intercepts of the following rational function $f(x)=\frac{x^{2}-7x + 10}{x^{2}+9x + 14}$

x - int: (-7,0) and (-2,0)
y - int: $(0,\frac{5}{7})$
x - int: (-2,0) and (-5,0)
y - int: $(0,-\frac{5}{7})$
x - int: (2,0) and (7,0)
y - int: $(0,-\frac{5}{7})$
x - int: (2,0) and (5,0)
y - int: $(0,\frac{5}{7})$

Explanation:

Step1: Find x - intercepts

Set $f(x)=0$, so $\frac{x^{2}-7x + 10}{x^{2}+9x + 14}=0$. Since a fraction is 0 when the numerator is 0 and the denominator is not 0. Solve $x^{2}-7x + 10=0$. Factor: $(x - 2)(x - 5)=0$. Then $x=2$ or $x = 5$.

Step2: Find y - intercepts

Set $x = 0$. Then $f(0)=\frac{0^{2}-7\times0 + 10}{0^{2}+9\times0+14}=\frac{10}{14}=\frac{5}{7}$.

Answer:

x - int: $(2,0)$ and $(5,0)$
y - int: $(0,\frac{5}{7})$