Questions: The graph of an exponential function is shown in the figure below. The horizontal asymptote is shown as a dashed line. Find the domain and the range. Write your answers as inequalities, using x or y as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.

The graph of an exponential function is shown in the figure below. The horizontal asymptote is shown as a dashed line. Find the domain and the range. Write your answers as inequalities, using x or y as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.
Transcript text: The graph of an exponential function is shown in the figure below. The horizontal asymptote is shown as a dashed line. Find the domain and the range. Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.
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Solution

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Solution Steps

Step 1: Find the domain

The domain is the set of all possible x-values. The graph extends infinitely to the left and to the right.

Step 2: Find the range

The range is the set of all possible y-values. The graph extends infinitely upwards, and approaches -3 without ever touching it.

Final Answer:

Domain: All reals Range: $y > -3$

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