Suppose a goalie allows a goal to be scored on the first shot they face. However, the goalie saves every shot they face after that. (Let's assume that the goalie has a long and historic career.) If the goalie has x-1 faced a total of a shots, the function P(x) = 100- gives the percentage of shots that the goalie x saved. You may graph the function with Desmos if it helps. I 1 2 4 5 8 10 20 25 40 50 100 200 P(x) 0 50 75 80 87.5 8~~~~~~ 90 ? ? ? ? ? ? 1. Find the value of P(100). 2. For what values of x is P(x) ≥ 98? (Give your answer using interval notation.) 3. Can P(x) ever be exactly equal to 100? No because the value of P(x) will always be less than 100 as a becomes very large. O Yes because the value of P(x) gets very close to 100 as a becomes very large. Yes because 100 is in the domain of P and its output value is 99. O No because 100 is not in the domain of P and its output is undefined.

Suppose a goalie allows a goal to be scored on the first shot they face. However, the goalie saves every shot they face after that. (Let's assume that the goalie has a long and historic career.) If the goalie has x-1 faced a total of a shots, the function P(x) = 100- gives the percentage of shots that the goalie x saved. You may graph the function with Desmos if it helps. I 1 2 4 5 8 10 20 25 40 50 100 200 P(x) 0 50 75 80 87.5 8~~~~~~ 90 ? ? ? ? ? ? 1. Find the value of P(100). 2. For what values of x is P(x) ≥ 98? (Give your answer using interval notation.) 3. Can P(x) ever be exactly equal to 100? No because the value of P(x) will always be less than 100 as a becomes very large. O Yes because the value of P(x) gets very close to 100 as a becomes very large. Yes because 100 is in the domain of P and its output value is 99. O No because 100 is not in the domain of P and its output is undefined.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Suppose a goalie allows a goal to be scored on the first shot they face. However, the goalie saves every
shot they face after that. (Let's assume that the goalie has a long and historic career.) If the goalie has
x-1
faced a total of a shots, the function P(x) = 100- gives the percentage of shots that the goalie
x
saved. You may graph the function with Desmos if it helps.
I
1
2
4
5
8
10
20
25
40
50
100
200
P(x)
0
50
75
80
87.5
8~~~~~~
90
?
?
?
?
?
?
1. Find the value of P(100).
2. For what values of x is P(x) ≥ 98? (Give your answer using interval notation.)
3. Can P(x) ever be exactly equal to 100?
No because the value of P(x) will always be less than 100 as a becomes very large.
O Yes because the value of P(x) gets very close to 100 as a becomes very large.
Yes because 100 is in the domain of P and its output value is 99.
O No because 100 is not in the domain of P and its output is undefined.

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