Question

Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q13

Answer 1

Step-by-step explanation

Finding the x-intercepts

To find the x-intercepts, we substitute y = 0 and solve for x.

`\begin{gathered} y=(x^2-25)/(x^2-16) \\ 0=(x^(2)-25)/(x^(2)-16) \end{gathered}`

The equation is equal to 0 if the numerator is equal to 0. Then, we solve the numerator.

`\begin{gathered} 0=x^2-25 \\ \text{ Add 25 from both sides} \\ 0+25=x^2-25+25 \\ 25=x^2 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ √(25)=√(x^2) \\ \pm5=x \\ \text{ Then} \\ x=5,-5 \end{gathered}`

Thus, the x-intercepts of the equation are the ordered pairs (5,0) and (-5,0).

Finding the y-intercepts

To find the y-intercepts, we substitute x = 0 and solve for y.

`\begin{gathered} y=(x^(2)-25)/(x^(2)-16) \\ y=(0^2-25)/(0^2-16) \\ y=(0^-25)/(0-16) \\ y=(25)/(16) \end{gathered}`

Thus, the y-intercept of the equation is the ordered pair (0,25/16).

Answer

The intercepts of the graph of the given equation are the ordered pairs (5,0), (-5,0), and (0,25/16).