Question
The function
is defined as follows. 4
(a) Find the domain of the function.
(b) Locate any intercepts.
© Graph the function.
(d) Based on the graph, find the range.
(a) The domain of the function
is
(Type your answer in interval notation.)
The function
(a) Find the domain of the function.
(b) Locate any intercepts.
© Graph the function.
(d) Based on the graph, find the range.
(a) The domain of the function
(Type your answer in interval notation.)
Ask by Mills Norris. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a)
The domain of is all real numbers, written as
The domain of
Solution
(a)
The domain of is the set of all real numbers, since both pieces of the function are defined for their respective intervals. In interval notation, the domain is
The domain of
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Extra Insights
The domain of the function
is all real numbers since both pieces of the piecewise function can accept values from negative infinity to positive infinity. Therefore, the domain in interval notation is
.
To locate intercepts, we find the
-intercept by setting
. Plugging this into the function gives
, thus the
-intercept is at
. Next, to find the
-intercept set
. For
,
gives
, and for
,
gives
. Therefore, the intercepts are at
and
.