Please divide into groups of three or four. Work these problems and discuss your answers together.
1. Consider the following graph where the domain is time and the range is the temperature of a
teapot.
a. What is different between what occurs on the interval [2,4] and the interval [0,2]?
b. Hypothesize what might be happening to the kettle at each point over the entire interval.
c. Create a new graph which would describe the temperature of a pot which begins heating at
time 2, begins to boil at time 6 and boils dry at time 10.
d. Create your own scenario for other groups to interpret what’s happening. Put your graph and
description on the board.
e. Interpret other groups’ graphs.
Consider the graphs:
a)
What is the range of h(x) on the domain [0,10]?
b)
What is the range of h(x) on the domain[4,10]?
c)
What is the range of h(x) on the domain [6,10]?
d)
What is f(g(h(10)))?
e)
What is h(g(f(10)))?
f)
What is f(g(h(0)))? Why?
g) Create two functions of your own with equations. Make one piecewise defined. Graph both
functions and verify that calculating f(g(x)) is the same on the graph and using the equation.
h) Create a function graph for a function f such that
i. f(f(f(0)))=3 (we write this as f3(0)=3)
ii. f4(1)=1 but f(1) 1
i)
Choose a secret number x. Create a graph for function f such that f(x)=5 and other groups will be
able to discover x. Then Create a graph for a function g such that g(x)=5 but other groups won’t
know for sure what x is. Put both graphs on the board.
j)
Interpret other groups’ graphs and find their values of x.