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 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:

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:

Answer

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible x - values. For an exponential function, there are no restrictions on the input x.

Step2: Determine domain

The domain of an exponential function is all real numbers. In inequality form, $x\in(-\infty,\infty)$ or $-\infty < x<\infty$.

Step3: Recall range definition

The range of a function is the set of all possible y - values. Looking at the graph, the horizontal asymptote is at $y = 1$ and the function approaches this value from above and then increases.

Step4: Determine range

The range of this exponential function is all y - values greater than 1. In inequality form, $y>1$.

Answer:

(a) $-\infty < x<\infty$ (b) $y > 1$