Question

can someone help me with this I need to find .the vertical asymptote, the horizontal asymptote , the x-intercept and the y-intercept

Answer 1

the vertical asymptote and horizontal asymptote

`\begin{gathered} f(x)=(x^2-1)/(x^2+3x+2) \\ f(x)=((x-1)(x+1))/((x+1)(x+2)) \\ f(x)=(x-1)/(x+2) \end{gathered}`

The vertical asymptote is x+2 = 0, x = -2

The horizontal asymptote is x - 1 = 0, x = 1

the x-intercept and the y-intercept

The intercept with x is calculated as 0 f(x)

`\begin{gathered} f(x)=0 \\ (x-1)/(x+2)=0 \\ (x-1)=0 \\ x=1 \\ \end{gathered}`

The intercept with x is (1,0)

The intercept with y is calculated for x = 0

`\begin{gathered} f(0) \\ (x-1)/(x+2) \\ (0-1)/(0+2) \\ (-1)/(2) \\ \end{gathered}`

The intercept with y is (0,-1/2)