Is y = 0 the asymptote of all functions of the form f(x) = ab^x? Explain your reasoning.

1 answer:

6 0

Y=0 would be a horizontal line. An asymptote is a line that a function approaches, but never reaches. Exponential functions such as these are a smooth curve. If both numbers are positive numbers greater than or equal to 1, the curve increases. If at least one of the numbers is a positive number between 0 and 1, the curve decreases. If a is a negative number, the curve decreases as well. If either a or b is zero, then the graph would stay constant at 0. However, as long as neither a nor b is zero, then this graph will never touch that point. The only way to get an answer of y=0 is to multiply by 0. If neither a nor b is zero, this won't happen.

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