e>
« back to results for ""
Below is a cache of http://instruct1.cit.cornell.edu/Courses/educ115/lab9.pdf. It's a snapshot of the page taken as our search engine crawled the Web.
The web site itself may have changed. You can check the current page or check for previous versions at the Internet Archive. Yahoo! is not affiliated with the authors of this page or responsible for its content.
NAME________________________ Problem Set # 9 LAB SECTION _______ EDUC 115 NAME________________________
Problem Set # 9
LAB SECTION _______
EDUC 115
Quiz 8 (April 12-13) will cover the following materials.
Course Packet: p. 92-103, Lab 9
Textbook: 1.5, 3.1
Additional practices from the textbook:
1.5: 15-20, 41-60, 83-85
3.1: 31-40, 51-56 (also find x-intercept and y-intercept)
#1. (8 points) Think about it:
i) Draw the graph of a one-to -one function that contains the line segments connecting
points (-2, -3), (0, 0), and (1, 5). Then draw the graph of its inverse on the same x-y
coordinates. Do these two graphs intersect? If yes, what are the coordinates of the
intersection point(s)?
ii) Draw the graph of f(x) = (2x-5)/(x+3). Solve for f
-1
(x). Then draw the graph of its
inverse on the same x-y coordinates. Do these two graphs intersect? If yes, what are the
coordinates of the intersection point(s)?
iii) Draw the graph of f(x) = -1/x. Solve for f
-1
(x). Then draw the graph of its inverse on
the same x-y coordinates. Do these two graphs intersect? If yes, what are the coordinates
of the intersection point(s)?
iv) Draw the graph of f(x) =3-

x
+
2 . Solve for f
-1
(x). Then draw the graph of its
inverse on the same x-y coordinates. Do these two graphs intersect? If yes, what are the
coordinates of the intersection point(s)?
v) Draw the graph of f(x) =

(x
+
1)
2
+
5. Solve for f
-1
(x). (Remember that you need to
restrict the domain of f(x) if it is not a one-to-one function. Make your restriction clear).
Then draw the graph of its inverse on the same x-y coordinates. Do these two graphs
intersect? If yes, what are the coordinates of the intersection point(s)?
vi) Does the graph of a one-to-one function have to intersect with the graph of its inverse
function? Explain.
vii) If the graph of a function and its inverse intersect, where must this necessarily occur?
Can they intersect anywhere else? Explain.
viii) Can a one-to-one function and its inverse be equal? What must be true about the
graph of f for this to happen? Explain. #2. (2 points) The current federal income tax is modeled by a complicated piecewise
function. Suppose the government came out with a new simplified version,
f(x)= 0.1x
if 0 x 10,000
0.2x-1000
if 10,000 x
where x is the amount of income earned and f(x) is the amount of tax owed
a) Describe what f
-1
(2000) represents.
b) Find f
-1
and include appropriate domains for this piecewise function