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# Evaluating composite functions: using graphs

Given the graphs of the functions f and g, Sal evaluates g(f(-5)).

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• , How did he get -2?
• First we try to solve for f(-5).
We know that y = f(x).
If y = f(x), then by asking what is the value of f(-5), we mean what will be the value of y if we take x as -5.
from the blue color graph we know that when x = -5, y = -2, Therefore we can say that if f(x) = y then f(-5) = -2.
Hope that helps!
• sorry, but how did he pick where the -2 point would match up on the graph? Looking back, couldn't 4 have had the same chance??
• You probably don't need this now but someone else might so.
I'm assuming this from when he solved f(-5).
To get this answer, you use the blue graph which is representing the values of f(x),
You get -5 on the x-axis and trace it down to where the blue curve intersects the line you traced down
When you trace the intersection point to the y-axis, you get -2 which is Sal's answer
• Isn't there another way to write g(f(-5))?
• At , how do we get that g(-2) is equal to one?
• When you look at the parabola for g(x), and find the point on that parabola where x = -2, you find that y = 1. So, g(-2) = 1
• Okay, so all this composite function things are very neat, but in the mathematical world, where would this come to use?
• In some lesson, before, there was a farming example. It takes crop yield and finds the total profit. Go look at that and think about it.
• where did you get -5? for f(x)
• He just picked that number randomly for the problem. Any number that could be graphed on the line y=f(x) would have worked just as well.
• given f(x)=-x+6 and g(x)=f(x+3), how to write an equation for function g?
• What does f(x+3) mean? well if instead you were doing say f(3), how would that look? well f(3) means plug in 3 for wherever there's an x in -x+6. so f(3) = -(3)+6 = 3.

So f(x+3) means plug x+3 in for x. so f(x+3) = -(x+3)+6 = -x - 3 + 6 = -x+3. So that means g(x) = f(x+3) = -x + 3. I hope this helped.
• What if we do (f+g)(4). How do we find that using only the graph?
• Well, I believe you are asking for f(g(4))...If so, you would look up g(4) from graph and find -2. Then look up f(-2) from graph and see that it is 4 and there you go. Hope this is useful to you...
(1 vote)
• How could I apply this to a real life scenario?