Question

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: (b) range:

Explanation:

Step1: Determine the domain

For an exponential function, there are no restrictions on the input values (x - values). The graph extends infinitely to the left and right, so the domain includes all real numbers.
Domain: All reals (or in inequality form, \( -\infty < x < \infty \))

Step2: Determine the range

The horizontal asymptote is a dashed line. From the graph, we can see that the function approaches the horizontal asymptote (y = -3, looking at the dashed line) but never goes below it. As x increases, the function values increase without bound. So the range is all real numbers greater than -3.
Range: \( y > -3 \) (or in interval notation, \( (-3, \infty) \))

Answer:

(a) domain: All reals
(b) range: \( y > -3 \)