Help! Calculus question. It is a picture of a graph and you have to do something to find something but I don't know. Please Help! I will post the picture below!

Question

Help! Calculus question.  It is a picture of a graph and you have to do something to find something but I don't know. Please Help! I will post the picture below!

anonymous · Answer

attachment

phi · Answer

they say 
h(x) =  f(g(x))

when x is 6
h(6) = f(g(6))

can you read what g(6) is ?  to find g(6), look at the g(x) graph, look along the x axis for 6, then go up until you hit the g(x) graph.  what y value do you get ?

anonymous · Answer

8

anonymous · Answer

What do I do next?

phi · Answer

yes, g(6) is 8
so 
h(6) = f( g(6) ) but g(6) is 8, so 
h(6) = f(8)

now we go to the f graph, look along the x-axis for 8, and go up until we reach the f graph.

that would give is f(8)  which is also h(6).

however they want h'(6)  (the slope of h at 6)
I would choose the slope of f at 8

anonymous · Answer

okay one minute

anonymous · Answer

on the f(x) graph it is almost 4 1/2

anonymous · Answer

so I jut need to find the slope at that point?

phi · Answer

true, but we want h'  (the little ' means derivative). In other words we want the slope of f at x=8
near x=8, f goes up at a specific slope  (change in y divided by change in x)

anonymous · Answer

could you help me find the slope?

phi · Answer

notice you have a line between x=7 and x=10
what is the change in y divided by the change in x ?

phi · Answer

if you need more info https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-relationships-functions/cc-8th-slope/v/slope-of-a-line