2/5/2021 Sophia :: Welcome
Score 14/18
You passed this Milestone
14 questions were answered correctly.
UNIT 3 — MILESTONE 3
4 questions were answered incorrectly.
1
The cost of a small business is given by the expression , where is the number of units produced.
The business will be profitable whenever its profit exceeds its cost.
If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 1/36
,2/5/2021 Sophia :: Welcome
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 2/36
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RATIONALE
The cost of a small business is given
by this expression, where is the
number of units produced. The
business will be profitable whenever
its profit, , exceeds the cost. To find
the corresponding graph, first
determine whether the profit region
lies above or below this boundary.
Since the business will be profitable
whenever its profit exceeds the cost,
we want the region ABOVE the
boundary line. This narrows our
choices to one of these two graphs.
Next, determine whether this is a strict
or non-strict inequality. In a strict
inequality, the shaded area cannot
equal the line, so the line is dashed.
With a non-strict inequality, the shaded
area can equal the line, so the line is
solid. The shaded area for profit must
exceed the cost, so the boundary line
must not be included. This indicates
that the situation must be represented
with a dashed line.
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 3/36
, 2/5/2021 Sophia :: Welcome
OR
This graph shows when the business is
profitable.
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 4/36
Score 14/18
You passed this Milestone
14 questions were answered correctly.
UNIT 3 — MILESTONE 3
4 questions were answered incorrectly.
1
The cost of a small business is given by the expression , where is the number of units produced.
The business will be profitable whenever its profit exceeds its cost.
If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 1/36
,2/5/2021 Sophia :: Welcome
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 2/36
,2/5/2021 Sophia :: Welcome
RATIONALE
The cost of a small business is given
by this expression, where is the
number of units produced. The
business will be profitable whenever
its profit, , exceeds the cost. To find
the corresponding graph, first
determine whether the profit region
lies above or below this boundary.
Since the business will be profitable
whenever its profit exceeds the cost,
we want the region ABOVE the
boundary line. This narrows our
choices to one of these two graphs.
Next, determine whether this is a strict
or non-strict inequality. In a strict
inequality, the shaded area cannot
equal the line, so the line is dashed.
With a non-strict inequality, the shaded
area can equal the line, so the line is
solid. The shaded area for profit must
exceed the cost, so the boundary line
must not be included. This indicates
that the situation must be represented
with a dashed line.
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 3/36
, 2/5/2021 Sophia :: Welcome
OR
This graph shows when the business is
profitable.
https://waldenu.sophia.org/spcc/college-algebra-3/milestone_take_feedbacks/7666406 4/36
