Math 623
Name___________________
FST 2.1-2.3 PRACTICE Quiz
SHOW ALL YOUR WORK and answer all questions thoroughly. [25 points total]
1.
State whether each relation below is a function or is not a function. [1 pt each]
4
3
2
1
-2
{ (4,1)
(3,4), (1,4), (2,5) (-1,4) }
a. ____YES______
2.
b. _____YES_____
c. _______NO___
Use the following functions to answer the questions below: [ 2 pts ea]
f(x) = 2x - 6
and
a.
f(2) = -2
b.
f(4) + g(-5) = 2 + 24 = 26
c.
d.
g(x) = x2-1.
g ( 4)
= 15/2 = 7.5
f ( 4)
Find the domain and the range of g(x)?
Domain:
All real numbers
Range:
All real numbers greater than or equal to
1.
or y ! "1
3.
Use the chart below to answer questions a through e:
Height (in feet)
Empire State Building (New York) 1250
Number of stories
102
John Hancock Tower (Boston)
Sears Tower (Chicago)
Nations Bank Plaza (Dallas)
61
110
72
52
Prudential Tower* (Boston)
•
788
1450
921
749
Does not include the 158 ft. “radio mast” on the Prudential’s roof.
a) Use height as the independent variable. Which axis should represent this variable? [2]
X axis
b) Draw a scatter plot of the points below. Plan the intervals on the X and Y axes so all the data
will fit. [4]
c.
Calculate the center of gravity and then plot it above.
[2]
(991, 77)
d.
Using the center of gravity and another point of your choosing, draw your best guess of
the line of best fit. Find the equation of the line you drew. (SHOW ALL YOUR
CALCULATIONS.)
[4]
multiple answers depend on which point chosen along with center of cravity:
33
y = 0.079x-1.11
or
+ 5.75
y=
459
e.
Without actually calculating it, describe below how you would find the “sum of the squares
of the errors.” [2]
Find the distance between each points y- value and y-value
directly above/below it on the line of best fit. Square each of these “errors” then add them up.
Answers may vary somewhat.