Question

3. For the function defined by

   25  6
x
f x ,
a) determine the equation of the horizontal asymptote.

Answer 1

To determine the equation of the horizontal asymptote of the function, we need to consider the limit of the function as x approaches positive infinity and negative infinity.

As x approaches positive infinity, the term 5x in the function becomes infinitely large compared to the constant term -6. Therefore, -6 becomes negligible in comparison, and the function approaches 2(5x) = 10x as x approaches positive infinity. So the equation of the horizontal asymptote is y = 10x.

As x approaches negative infinity, the term 5x in the function also becomes infinitely large (but negative) compared to the constant term -6. Again, -6 becomes negligible in comparison, and the function approaches 2(5x) = 10x as x approaches negative infinity. So the equation of the horizontal asymptote is also y = 10x.

Therefore, the equation of the horizontal asymptote for the function f(x) = 2(5x) - 6 is y = 10x.