Question

Jeremy likes to paint. He estimates the number of paintings he completes using the function, P(w) = 1/3w + 4, where w is the number of weeks he spends painting. The function J(y) represents how many weeks per year he spends painting. Which composite function would represent how many paintings Jeremy completes in a year?

a.) P[J(y)] = J(1/3w + 4)
b.) J[P(w)] = 1/3 ⋅ J + 4
c.) P[J(y)] = 1/3 ⋅ J(y) + 4
d.) J[P(w)] = J(1/3w + 4)

Answer 1

9514 1404 393

Answer:

c.) P[J(y)] = 1/3 ⋅ J(y) + 4

Explanation:

The function P takes a number of weeks as an argument and returns the number of paintings.

The function J takes some argument (unspecified) and returns a number of weeks per year.

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The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).

P(J(y)) = 1/3·J(y) +4 . . . . . matches choice C

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Additional comment

Looking at the units of the input and output of each of the functions is called "units analysis." It is a good way to solve many problems.