Using function concepts, it is found that:
- a) The y-intercept is y = 2.5.
- b) The horizontal asymptote is x = 3.
- c) The function is decreasing.
- d) The domain is
and the range is
.
- e) The graph is given at the end of the answer.
------------------------------------
The given function is:
------------------------------------
Question a:
The y-intercept is g(0), thus:
The y-intercept is y = 2.5.
------------------------------------
Question b:
The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.
--------------------------------------------------
Thus, the horizontal asymptote is x = 3.
--------------------------------------------------
Question c:
The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.
--------------------------------------------------
Question d:
- Exponential function has no restrictions in the domain, so it is all real values, that is
- From the limits in item c, the range is:
--------------------------------------------------
The sketching of the graph is given appended at the end of this answer.
A similar problem is given at brainly.com/question/16533631
