Question

Which graph represents the function f(x) = 2x/x^2-1

Answer 1

Graph B represents the function f(x).

Answer 2

The correct answer is B

Explanation:

Step 1

The first step in identifying the graph of the function is to determine where the vertical asymptotes occur. The vertical asymptotes occurs where the expression in the numerator is zero,

`x^2-1 =0\\(x+1)(x-1)=0\\\implies x=-1, x=1` .

The next step is to calculate the
`x` intercept. The
`x` intercept occurs where
`y=0`. We determine intercept as shown below,

`f(x)=(2x)/(x^2-1)=0\\ \implies 2x=0\\\\\implies x=0`

Step 2

The next step is to find the
`y` intercept. The
`y` intercept occurs when
`x=0`. We determine the
`y` intercept as shown below,

`(2(0))/(x^2+1) =0.`

The
`y` intercept occurs at
`y=0.`

Step 3

We now investigate the behavior of the function for different values of
`x`. We can tell that

,
`x>1,f(x)>0\\0<x<2,f(x)<0\\-1<x<0,f(x)>0\\x<-2,f(x)<0.`

Step 4

The only graph that has vertical asymptotes at
`x=1,x=-1` and that crosses goes through
`(0,0)` and meets all the conditions in Step 3 is the second graph B.