Homework 6 Due Wednesday September 23 at 10:00 PM
You only need to hand in Part I. Do not hand in Part II. You can check your answers to Part II in your
textbook. Problems from Part II or similar problems may appear on a future quiz.
Part I
1) Find the domain and range of each of the following functions.
a) f(x) = x
2
2 − 3
b)
f(x) = 1
(x − 3)2
c) f(x) = [x] + 1
2
d) f(x) = 2x
3 + 10
2) Find the domain of each of the following functions. You do not need to find the range.
a) f(x) = x
2 + 6x + 5
b)
f(x) = 1
x
2 + 6x + 5
d) f(x) = √
x
2 + 6x + 5
e)
f(x) = 1
√
x
2 + 6x + 5
.
3) In 2020 individuals who file federal tax returns that show income more than $40,126 and less than or
equal to $85,525 will pay federal income tax of 22%. Write a function that represents the income tax owed
for these individuals. Make sure to properly define your variables. What is the domain and range of this
function?
4) Suppose that d is the depth of the water in a bath tub in feet and t is time in minutes. Sketch the
general shape of a graph that describes the following scenario. You want to take a hot bath so you turn on
the hot water full blast and let it go for a while as the water warms up. After a time you notice that the
water is actually too hot, so while leaving the hot on full blast you now also add the cold water full blast.
When the tub is full you take a nice long hot bath. After you are done with your bath you pull the plug and
let the water out of the tub.
5) Let f(x) = x
2 find
f(x + h) − f(x)
h
simplify your answer as much as possible.
1
Part II
Do the following problems from the homework. DO NOT hand in these problems.
Section 2.3

1,3,5, 11, 15, 19, 33, 35, 55, 63, 71

Section 2.4

9,11, 43,47

Sample Solution