Find the Asymptotes y=3^x

Problem

y=3

Solution

1. Identify the type of function. The given equation y=3 is an exponential function with a base b=3 which is greater than 1

2. Check for vertical asymptotes. Exponential functions of the form y=bx 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.

(lim_x→−∞)(3)=0

4. Evaluate the limit as x approaches positive infinity.

(lim_x→∞)(3)=∞

5. Conclude that since the limit as x→−∞ is a constant value, a horizontal asymptote exists at that value.

Final Answer

Horizontal Asymptote: *y=0

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