please help me. :(

Question

Provide a detailed explanation as to why exponential function of the form y=a(b)* . (a > 0, b > 0, b ≠ 1) do not have x intercepts.

Answer 1

The exponential function y = ab^x where (a > 0, b > 0, b ≠ 1).

Where the parameter a is called function's  y intercept and the parameter b is called base of the function.

To find x intercept of any function substitute y = 0 in the function.

0 = ab^x

b^x = 0

Solution does not exist.

 

The domain of exponential function is all real numbers.

For x = 0, y = ab⁰

y = a

So the function y intercept is a .The range of all exponential functions is  all y > 0 if a is positive.

Note that y = 0 is not in the range. Thus all exponential functions have a horizontal asymptote at y = 0 and do not have any x intercepts.