The length of a rectangle is 50 meters. This is 6 meters more than twice the width. find the width
1 answer:
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2.
Domain: , because any value of
is allowed and gives a number
.
Range: , because
for any positive real
.
y-intercept: This is a point of the form . So plug in
; we get
. So the intercept is (0, 2), or just 2. (Interestingly, you didn't get marked wrong for that...)
Asymptote: This can be deduced from the range; the asymptote is the line .
Increasing interval: Going from left to right, there is no interval on which is increasing, since 1/4 is between 0 and 1.
Decreasing interval: Same as the domain; is decreasing over the entire real line.
End behavior: The range tells you , and you know
is decreasing over its entire domain. This means that
as
, and
and
.
3.
Domain: Same as (2), .
Range: We can rewrite .
for all
, so
for all
. Then the range is
.
y-intercept: We have , so the intercept is (0, -6) (or just -6).
Asymptote:
Increasing interval: Not increasing anywhere
Decreasing interval:
End behavior: Similar to (2), but this time as
and
as
.