Exercise 12 Page 965

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!

y=ax+b/x-1

SubstituteII

y= -1, x= 0

-1=a* 0+b/0-1

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Solve for b

Multiply

Multiply

-1 = b/0-1

SubTerms

Subtract terms

-1 = b/-1

MultEqn

LHS * (-1)=RHS* (-1)

1=b

RearrangeEqn

Rearrange equation

b=1

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.

y=ax+1/x-1

SubstituteII

y= 1, x= 2

1=a* 2+1/2-1

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Solve for a

SubTerms

Subtract terms

1=a* 2+1/1

CalcQuot

Calculate quotient

1=a* 2+1

SubEqn

LHS-1=RHS-1

0=a* 2

MultEqn

LHS * 2=RHS* 2

0=a

RearrangeEqn

Rearrange equation

a=0

With the values of a and b, we can complete our function. y=0* x+ 1/x-1 ⇔ y=1/x-1 Therefore, the answer is option F.