Composition of Functions
Analyzing Graphs
Inverse Functions/Relations
100
Find (f+g)(x)
x2+2x+4
100
Find the domain and range for g(x)
Domain:
(-oo, oo)
Range:
[-3, oo)
100
What is the relationship between a function and its inverse? Can you use the words 'input' and 'output'?
The inverse function undoes everything the original function does. The output of the original function becomes the input of the inverse function.
200
Find f(g(x))
2x2+4
200
State the positive intervals of f(x)
(2,8]
200
Describe functions and their inverses using the gift wrap function and inverse gift wrap function.
The gift wrap function wraps a gift by first inputting a box, wrapping, putting on bow, then outputs wrapped gift. The inverse gift wrap function inputs wrapped gift, takes off bow, unwraps wrapping paper, then outputs a box.
300
Find (f-h)(3)
9
300
Evaluate (g+f)(0)
-4
300
Find
f^-1(x) if f(x)=4x-12
y=(x/4)+3
400
Find
(f@g)(2)
12
400
Find
(f@g)(-5)
0
400
Graph the function
f(x)=4x-12 text( and its inverse ) f^-1(x)=(x/4)+3
500
Find
(g@h)(-1)
9
500
Find
(f/g)(0)
1/3
500
Noah throws a rock off a cliff. The function
f(t) = -.2t^2+10
tells us the time (t) the rock has been in the air and the height f(t) of the rock. What does the inverse function represent in regards to the problem situation?
The original function would tell you the height of the rock if you were told the time the rock was in the air. The inverse function would give you the time the rock was in the air if you were given the height.