Find the Asymptotes y=4^x

Problem

y=4^x

Solution

1. Identify the type of function. The given equation y=4^x is an exponential function with a base b=4 which is greater than 1

2. Check for vertical asymptotes. Exponential functions of the form y=b^x are defined for all real numbers x so there are no vertical asymptotes.

3. Analyze the end behavior as x approaches infinity. As x→∞ 4^x→∞ so there is no horizontal asymptote to the right.

4. Analyze the end behavior as x approaches negative infinity. As x→−∞ the expression becomes 4^(−∞) which is 1/4^∞

5. Calculate the limit. Since 1/4^∞ approaches 0 the line y=0 is a horizontal asymptote.

Final Answer

Horizontal Asymptote: *y=0

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