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## Algebra (all content)

### Course: Algebra (all content)>Unit 7

Lesson 18: Modeling situations by combining and composing functions (Algebra 2 level)

# Modeling with composite functions

Sal determines the correct functions to compose (and the correct order) in order to model a given relationship, and vice versa.

## Want to join the conversation?

• So, could it be phrased as (H°T)(r)? Or how would it be formatted in that form?
• That is the correct format
• Why wouldn't the answer be T(H(k))?
• You need to match up the correct input/output values. Remember, the inner function is done 1st and then the output of the inner function is used as input to the outer function.

Sal is creating a function that defines the "height of the tree as a function of its altitude".
This means the input to the function is "altitude" and the output needs to be "height of the tree".
Which function has an output of "height of tree". Its H. So, this has to be the outer function.
Which function has an input of "altitude"? Its T. So, we have to use function T 1st. It creates as output "the average temperature", which happens to be the input for H.

If you tried to do T(H(k)), it won't work. Function H comes first. The input for H has to be temperature, but Sal needs an input that is "altitude".
Hope this helps.
• why isn't the answer B(H(k)) for the second problem?
(1 vote)
• The output for B is "number of birds nesting ...", but the question asks for a final output as "height of tree...".
So the final function applied has to be H, not B.
And the question indicates that the initial input is "altitude of a specific location", so that points to function T as the first function.
• So why can "the average number of fans per game as a function of the number of rainy days in a season" be written as "N(W(P(r))", while "the average number of fans per game as a function of the team's average daily practice time" is written "N(W(x))". Shouldn't there be another w in the latter function as it is called, "N(w)" in the problem?
• You are correct that N(W(P(r))) is the average number of fans per game as a function of the number of rainy days in a season. You are also correct that N(W(x)) is average number of fans as a function of teams daily practice time. I know alot of variables are being thrown around here and it looks confusing but N(w) could have been written with any name for the independent variable w. When we decided to substitute in W(x) for the independent variable w in N(w), the "w" went away in N(w) and was replaced by W(x). Now you could say N(W(x)) = N(x) if you wish.
• How is H(T(r)) the answer? T(r) represents the "average temperature at that location" not altitude? Shouldn't the answer be H(r)?
(1 vote)
• You are looking for height as a function of altitude, T(r) shows the average temperature at that location as a function of it's altitude, then you put that function into H, it is still a function of altitude though because T(r) is a function of altitude.
(1 vote)
• To clarify, when Mr. Khan says "the height of the tree as a function of its altitude" (), what does it mean to be "as a function", and how does that correlate into having the input as the altitude?
(1 vote)
• The phrase "the height of the tree as a function of its altitude" tells you the output of a function is the height and the function accepts altitude as its input. In other words, the functions will calculate the height of the tree when you input the tree's altitude.
(1 vote)
• In the video at when sal is discussing the secong example he does not discuss the choices but if we were to solve them is it possible to solve H(B(r)) and T(K(h)) when we can't input r into B as the only input of B is x? Are we going to say it is unspecified?
(1 vote)
• like there are inverse trig functions like arcsine(sin^-1) and cossine(cos^-1) is there something as a inverse function
(1 vote)
• So there are inverse functions. An inverse function just inverse of a function. In fact sin^-1 is the inverse function of sine. You could also take the inverse of non-trigonometric functions.

There should be a section on Khan Academy.
(1 vote)
• At about minutes into the video, Sal wrote N(W(P(r))), isn't it supposed to be N(P(r))?
(1 vote)
• The functions B,H and T aren't related so, How can we compose H(T(r))?
(1 vote)
• But they are related. T outputs average temperature at a point, and H takes average temperature as its input.
(1 vote)