Use this explore combinations and compositions of functions. My goal is to have them look at and compare domian of the different combinations and compositions but, I think there is a lot more you can learn from this activity.

I. Complete the three things below, for each of the following pair of functions.
1. Find the domain of f and the domain of g by looking at the graph and the table on the left.
2. Find the domain of each of the following by looking at the graph and the table on the left.
i. f+g and g+f How does the domain of each compare to the domain of f and g.
ii. f-g and g-f
iii. fg and gf
3. How does the domain of each compare to the domain of f and g.
4. Generalize the method of finding the domain for each of the above combinations f+g, f-g fg, etc.
a. enter x^2+3 in for f(x) and x+1 in for g(x)
b. enter x^2+3 in for f(x) and log(x+1) in for g(x)
c. enter x^2+3 in for f(x) and sqrt(x+1) in for g(x)
d. enter x^2+3 in for f(x) and 1/x+1 in for g(x)
e. enter x^2+3 in for f(x) and 2^(x+1) in for g(x)
f. enter x^2+3 in for f(x) and abs(x+1) in for g(x)
g. enter x^2+3 in for f(x) and 1 / (1 + e^(-(x + 1))) in for g(x)
h. Now mix and match any of the functions above or create your own from the functions family’s.
II. Now repeat the above process with a few of the functions f and g for f/g and g/f until you can Generalize the method of finding the domain for each.(You may need to scroll over to see the table data.)
III. Complete the following.
1. Find the domain of each of the following by looking at the table on the left or by studying the graph for the given functions.
i. Find the domain of f(g(x)).
ii. Find the domain of g(f(x)).
2. How does the domain of each compare to the domain of f and g.
3. Generalize the method of finding the domain for each.(You may need to scroll over to see the table data.)
a. Pick a function f and g from above and enter them into the function fields.
b. Enter 1/(x^2) in for f(x) and sqrt(x+1) in for g(x)
c. Enter 1/(x^2) in for f(x) and sqrt(x-1) in for g(x)