# 1.3 Graphs of Functions

```Reminder
• Quiz corrections for Ch. 2 due this
Thursday.
HWQ
For the function
find the following:
5 x3  15 x 2  20 x
f  x 
x 2  x  12
State asymptotes as equations of lines and intercepts as
ordered pairs.
a) Vertical Asymptotes and holes
b) Horizontal (or) Slant Asymptotes
c) X-intercepts
d) Y-intercepts
e) Domain
Students will classify scatter plots.
Students will use scatter plots and a graphing
utility to find quadratic models for data.
Students will choose a model that best fits a
set of data.
Example 1
Decide whether each data set would best be modeled by a
linear model or a quadratic model.
•
a) (1, 3), (2, 5), (4, 6), (6, 8), (8, 9), (10, 10), (12, 13)
a ) linear model
•
b) (2, 1), (4, 2), (6, 4), (8, 7), (9, 10), (11, 15), (13, 20)
Enter both sets of data into a graphing utility and display
the scatter plots.
Example 2
The following table gives the mileage y, in miles per gallon, of a
certain car at various speeds x (in miles per hour).
a) Use a graphing utility to create a scatter plot of the data.
b) Use the regression feature of a graphing utility to find a quadratic
model that best fits the data.
c) Use the model to predict the speed that gives the greatest
mileage.
Speed, x Mileage, y
10, 21.3
45, 31.9 b) y  .012 x 2  .948 x  12.285
15, 23.7
50, 29.5
20, 25.9
55, 27.6 c) Maximum @  39.5,31
25, 27.6
60, 25.3
Speed that gives the greatest
30, 29.4
65, 23.0
mileage is 39.5 mph.
35, 31.0
70, 20.0
40, 31.7
P  0.132t 2  1.901t  6.872
The following table gives the monthly normal precipitation P (in
inches) for San Francisco, California.
a) Use a graphing utility to create a scatter plot of the data. Let t
represent the month with t=1 corresponding to January.
b) Use the regression feature of a graphing utility to find a
quadratic model that best fits the data.
c) Graph the model with the scatter plot from part b.
d) Use the model to predict the precipitation in San Francisco
on September 15th.
Month t
Precip. P
Month t
Precip. P
January
4.45
July
.03
February
4.01
August
.07
March
3.26
September
.20
April
1.17
October
1.04
May
.38
November
2.49
June
.11
December
2.89
Polynomial application
• An open box is to be made from an 8x11
piece of cardboard by cutting equal squares
with sides of length x from the corners and
turning up the sides.
• a) find an expression for the volume of the
box as a function x.
• b) find the x-value for which V(x) is a
maximum.
Polynomial application
• Find two positive real numbers whose
product is a maximum and where the sum
of the first and three times the second is 42.
Polynomial application
You have 40 feet of fence to enclose a rectangular garden
along the side of a barn. What dimensions produce the
maximum area? What is the maximum area that you can
enclose?

You Try:
A rancher has 200 feet of fencing with which to enclose
two adjacent rectangular corrals. What dimensions
should be used so that the enclosed area will be a
maximum?
Homework
• Chapter 2 Practice test (Pg 99 in solution
manual) – (Pg 533 Answers in solution
manual)
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