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. (a) range: (b) domain:

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. (a) range: (b) domain:

Answer

Explanation:

Step1: Recall the definition of domain

The domain of a function is the set of all possible input values (x - values). For any exponential function of the form (y = a\cdot b^{x}+k), there are no restrictions on the value of (x).

Step2: Recall the definition of range

The range of a function is the set of all possible output values (y - values). For an exponential function (y = a\cdot b^{x}+k), if (b>1) and (a>0), the horizontal asymptote is (y = k). The function (y) approaches the horizontal asymptote as (x\to-\infty) and increases without bound as (x\to+\infty). From the graph, the horizontal asymptote is (y = - 2), and the function is above the horizontal asymptote.

Answer:

(a) range: (y>-2) (b) domain: All reals