the graph of an exponential function is shown in the figure below. the horizontal asymptote is shown as a…

the graph of an exponential function is shown in the figure below. the horizontal asymptote is shown as a dashed line. find the range and the domain. 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 range and the domain. 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.

Answer

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible input - values (x - values). For an exponential function, there are no restrictions on the x - values. All real numbers are valid inputs.

Step2: Recall range definition

The range of a function is the set of all possible output - values (y - values). Looking at the graph, the horizontal asymptote is at y = 4. The function values are all real numbers less than 4.

Answer:

Domain: $x\in(-\infty,\infty)$ or $-\infty<x<\infty$ Range: $y < 4$