Question

graphing exponential functions & key features
question 7 of 8 (2 points) | question attempt: 1 of 3
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: all reals
(b) range: ( y>-2 )

Explanation:

Step1: Analyze the domain

The domain of a function is the set of all possible input values (x - values). For an exponential function (and most functions graphed like this one), there are no restrictions on the x - values. So, \(x\) can be any real number.

Step2: Analyze the range

The range of a function is the set of all possible output values (y - values). Looking at the graph, there is a horizontal asymptote at \(y=-2\). The function approaches \(y = - 2\) but never actually reaches it (as indicated by the dashed line), and the function values are above \(y=-2\). So, \(y>-2\)

Answer:

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