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