Find the Asymptotes f(x)=5^x

Problem

ƒ(x)=5^x

Solution

1. Identify the type of function. The function ƒ(x)=5^x is an exponential function with a base b=5 where b>1

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

3. Evaluate the limit as x approaches negative infinity to find horizontal asymptotes. As x→−∞ the expression 5^x approaches 0

(lim_x→−∞)(5^x)=0

4. Evaluate the limit as x approaches positive infinity. As x→∞ the expression 5^x grows without bound.

(lim_x→∞)(5^x)=∞

5. Conclude that a horizontal asymptote exists at the value the function approaches as x goes to negative infinity.

Final Answer

Horizontal Asymptote: *y=0

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