Functions f(x) and g(x) are shown below: f(x) g(x) f(x) = −4(x − 6)2 + 3 graph of cosine function which starts at 0 comma 2 and
increases to the maximum at pi over 2 then decreases to the minimum at 2 pi where the cycle repeats Courtesy of Texas Instruments Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value.
1 answer:
Since f(x) is written in vertex form with a negtive vertical expansion factor, we know it opens downward and the maximum is at the vertex, 3.
Since we have a graph of g(x), we can read the maximum from the graph, 4.
We can determine which function has the largest maximum by noting that the largest maximum is 4 and that it corresponds to function g(x).
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Answer:
750 < p < 1500
Step-by-step explanation:
The total cost of the affair for p attendees is ...
750 +2.25p
The average cost is that number divided by p. The answer choices suggest that "between" means that the cost per person cannot be 2.75 or 3.25. Applying the limits to the average cost, we get ...
2.75 < (750 +2.25p)/p < 3.25
2.75 < 750/p + 2.25 < 3.25 . . . . . . . . separating the fraction parts
0.50 < 750/p < 1.00 . . . . . . . . . . . . . . subtract 2.25
2 > p/750 > 1 . . . . . . . . . . . . . . . . . . . . . take the reciprocal*
1500 > p > 750 . . . . . . . . matches choice 4
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* Taking the reciprocals of numbers with the same sign reverses their order:
2 < 3 but 1/2 > 1/3
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An alternate approach to the solution would be to multiply by p:
0.50p < 750 < 1.00p
To solve this requires it be made into two inequalities:
0.50p < 750 ⇒ p < 1500
and
750 < 1.00p ⇒ 750 < p
Then these would need to be recombined to form the answer:
750 < p < 1500
