We want to find the function that is best represented by the given graph.
Notice that this is a rational function with a vertical asymptote at x= 1. This means that the function is undefined for x= 1. By knowing this we can write the denominator of our equation.
x=1 ⇒ x-1=0We need to have (x-1) as a product in the denominator. This eliminates the options G and I. Now, let's write our partial equation considering the remaining options F and H.
y = ax+ b/x-1
Since we know the y-intercept ( 0, -1), we can find the value of b by substituting x= 0 and y= -1 into the above equation. Let's do it!
We found that the value of b is equal to 1.
y=ax+ 1/x-1
Next we will use the other point, (2,1), to find the value of a. Let's substitute x= 2 and y= 1 into the above equation and solve for a.
