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Vertical Line Test of Functionality
Symmetry of a Function
Using the Calculator to Evaluate Graphs
2.2 The Graph of a Function
Recall -
Function –
A relation in which each value of the independent
variable corresponds to exactly one value of the
dependent variable
On a graph, what does it look like if a particular
value of the independent variable has more than
one value for the dependent variable?
The Vertical Line Test of Functionality
If a vertical line drawn anywhere over the graph
of a relation intersects the relation at exactly one
point, the relation is a function.
Is it a function?
(-8, -3)
(9,5)
{ | 8 9}x x
{ | 3 5}y y
Is it a function?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)
{ | 8 8}x x
{ | 7 6}y y
What are the x-intercepts?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)
( 7, 0)
(2, 0)
(6, 0)
What is the y-intercept?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)(0, 5)
Find f(-4)
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)( 4) 6f
Find f(1)
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6) (1) 2f
Is f(0) positive or negative?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6) (0) 5f
Is f(-3) positive or negative?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)( 3) ?f
For what numbers x is f(x)>0?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)
[ 8, 7)
and
(2, 6)
For what numbers x is f(x)<0?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6) ( 7, 2)and
(6, 8]
For what values of x does f(x)=-
2?
(8,-2)
(6,0)(4,1)
(2,0)
(1,-2)
(0,-5)
(-2, -7)
(-4,-6)
(-5,-4)
(-7,0)
(-8,6)
( ) 2
when
6, 1, 8
f x
x
Symmetric about the y-axis
The function is a reflection of itself about the line
x = 0.10
8
6
4
2
-2
-4
-8 -6 -4 -2 2 4 6 8
Symmetric about the origin
If the graph is rotated 180⁰ about the origin, it will look the same as the original picture.
0.8
0.6
0.4
0.2
-0.2
-0.4
-0.6
-0.8
-2 -1.5 -1 -0.5 0.5 1 1.5 2
Calculator
The function C represents the cost (in dollars) per
passenger of a flight on a Boeing 747 across the
Atlantic Ocean (3000 miles) with an airspeed of
500 mph as a function of the number of
passengers, x, traveling.
Graph the function in your calculator and find a
“good” viewing window.
36, 000( ) 100
10
xC x
x
Calculator36,000
( ) 10010
xC x
x
36, 000( ) 100
10
xC x
x
What is the cost per person for 100 passengers?
Press “2nd”, “TRACE” (CALC), “1” (value)
What is the cost per person for 145
passengers?
The airline wants to run a special and charge only $350
per person for the flight. How many seats do they have
to sell to cover their costs?
p. 75 # 2 - 9, 11 - 21 odd, 29,
37 - 38
Assignment
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