Question
- Higher Order Thinking Consider the functions
and
for the domain
.
a. Without evaluating or graphing the
functions, how do the ranges compare?
a. Without evaluating or graphing the
functions, how do the ranges compare?
Upstudy AI Solution
Tutor-Verified Answer
Answer
The range of
is
and the range of
is
. The range of
is entirely below the range of
.
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Bonus Knowledge
Both functions
and
are linear, with
having a slope of 2 and a y-intercept of 1, while
has the same slope but a y-intercept of 2. Since both have the same slope, they will be parallel lines on a graph. Over the domain
,
will produce values ranging from 1 to 11, and
will produce values ranging from 2 to 12. Therefore, the range of
will always be shifted up by 1 unit compared to the range of
.
In summary, while the ranges of both functions overlap in their respective spans,
's range will consistently be 1 unit higher for all corresponding values of
in the same domain.