Question

Which graph(s) have a horizontal asymptote at y=7? Select all that apply.

A. y = 7/x-2
B. y = (7x²+1)/(x²+7)
C. y = 7+ (1/x)
D. y = (7x+3)/(x²+1)​

Answer 1

The graph(s) that have a horizontal asymptote at y=7 is option B). y = (7x²+1)/(x²+7).

Step-by-step explanation:

To find the graph(s) that have a horizontal asymptote at y=7, we need to examine the equations given.

A. y = 7/x-2: This equation does not have a horizontal asymptote at y=7 because as x approaches infinity or negative infinity, the value of y approaches 0, not 7.

B. y = (7x²+1)/(x²+7): This equation does have a horizontal asymptote at y=7. As x approaches infinity or negative infinity, the value of y approaches 7.

C. y = 7+ (1/x): This equation does not have a horizontal asymptote at y=7 because as x approaches infinity or negative infinity, the value of y approaches 7 with an additional term of 1/x.

D. y = (7x+3)/(x²+1): This equation does not have a horizontal asymptote at y=7 because as x approaches infinity or negative infinity, the value of y approaches 0, not 7.

Therefore, the graph(s) that have a horizontal asymptote at y=7 are B. y = (7x²+1)/(x²+7).