QuestionFinding domain and range from the graph of an exponential function
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. (a) domain: $\square$ (b) range: $\square$ Explanation Check

Studdy Solution

STEP 1

1. The graph represents an exponential function.
2. The horizontal asymptote is at $y = -4$ .
3. The curve rises steeply to the right.

STEP 2

1. Determine the domain of the exponential function.
2. Determine the range of the exponential function.

STEP 3

The domain of an exponential function is typically all real numbers because exponential functions are defined for every real number $x$ .

STEP 4

The range of an exponential function is determined by its horizontal asymptote and the direction in which the function moves. Since the horizontal asymptote is at $y = -4$ and the function rises steeply to the right, the range is all real numbers greater than $-4$ .
The domain and range are:
(a) domain: $\text{All reals}$ or $x \in (-\infty, \infty)$
(b) range: $y > -4$

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