Chapter 4.3, Problem 1AYU

To determine

To calculate:

The intercept value of the following equation:

  $y=\frac{x^2-1}{x^2-4}$

Answer to Problem 1AYU

The intercepts of graph of the equation $y=\frac{x^2-1}{x^2-4}$ are $\left(1,0\right)$ and $\left(0,\frac{1}{4}\right)$ .

Explanation of Solution

Given information:

  $y=\frac{x^2-1}{x^2-4}$

Formula Used:

Intercepts:

  $y-$ Intercept: Set $x=0\backslash \text{displaystyle}x=0x=0$

  $x-$ Intercept: Set $y=0\backslash \text{displaystyle}y=0y=0$

Calculation:

Know that:

  $y=\frac{x^2-1}{x^2-4}$

To find $x-$ intercept by definition set $y=0$ and solve the equation for $x,$ as well as to find $x-$ intercept, set $x=0$ and solve the equation for $y$ .

  $x-$ intercept:

  $0=\frac{x-1}{x^2-4}\Rightarrow x-1=0\Rightarrow x=1$

  $y-$ intercept:

  $y=\frac{0-1}{0^2-4}\Rightarrow \frac{-1}{-4}=\frac{1}{4}$

Hence, the intercepts are $\left(1,0\right)$ and $\left(0,\frac{1}{4}\right)$