Pls i really need your help. i dont have any idea how to make a word problem for COMPOSITE FUNCTIONS. can you give a sample? THANKS GOD BLESS..
Suppose the temperature recorded by a weather balloon is a function of height, T= f(h) (if you want a specific function, just put in any function you like for f), and that the height of the balloon is a function of time, h= g(t). Then the temperature, as a function of time, it the composite function, $\displaystyle T= f\circ g(t)= f(g(t))$.
Now, do you understand what that means? That is far more important than just giving an answer.
Hello, jilian!
Make a word problem for composite functions. Can you give a sample?
I like HallsofIvy's example!
I think of composite functions as "machines" (number crunchers) in a row.
The first is a machine that converts time $\displaystyle (t)$ into height $\displaystyle (h).$
. . $\displaystyle t \;\to\;\boxed{\begin{array}{c}\text{Height} \\ h(t) \end{array}}\;\to\; h $
The second is a machine that converts height $\displaystyle (h)$ into temperature $\displaystyle (T).$
. . $\displaystyle h \;\to\;\boxed{\begin{array}{c}\text{Temp.} \\ T(h) \end{array}} \;\to\;T$
Placing the machines in sequence, we have:
. . $\displaystyle t \;\to\; \boxed{\begin{array}{c}\text{Height} \\ h(t) \end{array}} \;\to\;h\;\to\;\boxed{\begin{array}{c}\text{Temp.} \\ T(h) \end{array}}\;\to\;T $
If this were an "assrmbly line" in our "factory",
. . it would be practical and economical to have one machine to do the job.
. . $\displaystyle t \;\to\;\boxed{\begin{array}{c} T(h(t)) \end{array}} \;\to\;T $
This would convert time $\displaystyle (t)$ directly to temperature $\displaystyle (T)$.