# 1.2 Graphing Utilities and Complete Graphs x ```Pg. 11/21 Homework
• Pg. 21 #20 – 29
Pg. 30 #1 – 13 odd, 14 – 30 even
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#11 8
#12 5
#13 5  3
#14 5  2
#15 12 #16 7
#17 4
#18 8
#19 4  x
#20 3  x or 3  x
#7 -\$10.75, \$8.00, \$26.75, \$70.50
#8 y = 0.25x – 35.75
#9
Graph
#10 break even = 143 tickets; x &gt; 143 will yield a profit
• Solve and write in Set Notation
8  3x  2  7
x  1 or x  2
1.2 Graphing Utilities and Complete Graphs
Problem Solving
• State the problem in your
own words
• Define the variables in the
problem
• Clearly identify what you
are given and what you are
looking for
Example
• It costs \$8 to enter the fair.
Each ticket towards a ride
costs \$0.75.
• Generalize the pattern from
the given information.
1.2 Graphing Utilities and Complete Graphs
• The roller coaster requires 6
tickets to ride. How much
money total will you spend
to ride the roller coaster
twice?
• You only have \$20. You want
to ride the Tilt-a Whirl twice
and roller coaster once. If
the Tilt-a Whirl requires 5
tickets. Will you have any
money left over for cotton
candy?
1.2 Graphing Utilities and Complete Graphs
Table of Values/Data Pairs
Graph
1.2 Graphing Utilities and Complete Graphs
Proper Windows
• Find a proper window for:
y  x 2  10
y  x  20
Sketches of Complete Graphs
• Must contain all data from a
given table
• Must suggest a pattern from
the table
• The equation must model
the data for every point in
the table
• This gives one possible
complete graph through the
points in the given table
1.2 Graphing Utilities and Complete Graphs
x
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
y
-15
-5.625
0
2.625
3
1.875
0
-1.875
-3
-2.625
0
5.625
15
y  x3  4 x
1.3 Functions
Functions
• A function of x is a
correspondence that
associates each x in a set X
with exactly one y in a set Y.
– If x is the input value and y is
the output value we call y the
image of x under f.
• For all functions: y  f  x 
• All functions must pass the
VLT!!
• Functions can be graphed
• Functions are equations in
two variables
• All functions have a domain
and range
1.3 Functions
Function Values
• Find the function values
f  x   x 2  3x
f  2 
f  x  1
Are the following functions?
1.3 Functions
y  x2  4
y  x2  4
• Graph the function
• Graph the function
• Find the domain and range
• Find the domain and range
1.3 Functions
Determine the domain and range.
Use a grapher if necessary.
y  x2
x
y
x 1
5
y
x 1
y
1
x
```