Find the Asymptotes q(x)=1.5^x

Problem

q(x)=1.5

Solution

1. Identify the type of function. The function q(x)=1.5 is an exponential function of the form ƒ(x)=bx where the base b=1.5 is greater than 1

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

3. Evaluate the limit as x approaches infinity. As x→∞ 1.5→∞ so there is no horizontal asymptote to the right.

4. Evaluate the limit as x approaches negative infinity. As x→−∞ the expression becomes 1.5(−∞) which is equivalent to 1/1.5

5. Determine the horizontal asymptote. Since 1/1.5 approaches 0 the line y=0 is the horizontal asymptote.

Final Answer

Horizontal Asymptote: *y=0

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