chapter 01 – section 08 a preview of graphs and functions

Chapter 01 – Section 08

A Preview of Graphs and Functions

© William James Calhoun

To interpret graphs in real-world settings, and to sketch graphs for given functions.

Age of Car(year)

ApproximateValue of Car

0 $15,0001 $11,0002 $8,0003 $6,0004 $5,0005 $4,000

This can also be shown in a graph.

Car Depretiation Over Five Years

02468

10121416

0 2 4 6

Age of the Car (years)

App

roxi

mat

e V

alue

of

Car

(th

ousa

nds

of d

olla

rs)

The dollar value of a car begins to decrease immediately after it leaves the lot. This is called depreciation.

• depreciation = original cost of car - value of car when sold

The following table shows how a typical $15,000 car depreciates.


Graphing Terms:

• function - a relationship between input and outputthe output depends on the input and there is only one output for every input

• vertical axis - the upward axisrepresents current car value from the sample graph

• horizontal axis - the sideways axisrepresents age of car from the sample graph

• ordered pair - a pair of numbers used to locate points on a graphexamples from the sample graph are: (2, 8), (1, 11), and (3, 6)in ordered pairs, the horizontal # always comes first

• origin - the point on a graph where all values are zeroGenerally, this is the point (0, 0).


0

1

2

3

4

5

6

7

8

9

1 2 3 4 5

Horizontal Axis

Vertical Axis

Origin

Function - the equation being graphed by the purple line

(1, 6)

(2, 1)

(3, 2)

(5, 3)

Ordered Pairs

(4, 8)

Here is a labeled diagram of a graph.


EX1EX1β

EXAMPLE 1α: Shim owns a farm market. The amount a customer pays for sweet corn depends on the number of ears that are purchased. Shim sells a dozen ears of corn for $3.00.a. Make a table showing the price of various purchases of sweet corn.b. Write four ordered pairs that represent the number of ears of corn and the price of the corn.c. Describe a set of axes that could be used to graph the number of ears of corn and the price of the corn.d. Draw a graph that shows the relationship between the number of ears of corn and the price.e. As you read the graph from left to right, describe the trend you see. Explain.

This example will spread across the next few slides.


EX1EX1β

a. Make a table showing the price of various purchases of sweet corn.Number of Dozen Ears of Corn Price

0.5 6 $1.501 12 $3.00

1.5 18 $4.502 24 $6.00

Sample amounts chosen were:

0.5, 1, 1.5, and 2 dozen

b. Write four ordered pairs that represent the number of ears of corn and the price of the corn.

Get this information from the chart.ordered pair = (ears of corn, price)(6, 1.5), (12, 3), (18, 4.5), (24, 6)

c. Describe a set of axes that could be used to graph the number of ears of corn and the price of the corn.Let the horizontal axis represent the number of ears of corn, and let the vertical axis represent the price of the corn.


EX1EX1β

d. Draw a graph that shows the relationship between the number of ears of corn and the price.First, draw the axes. Second, choose the scale of the axes. Third, draw the scale. Finally, plot the points.

First, draw the axes.Second, choose the scale of the axes.

6

3

4 8 12 16 20 24

Third, draw the scale. Price only goes up to $6.00, so from $0 to $6.

Number of Ears ranges from 0 to 24.This sets the max & min values.

0

Number of Ears

Pri

ce (

in $

)

Finally, plot the points.

(6, 1.5)(12, 3)(18, 4.5)(24, 6)

e. As you read the graph from left to right, describe the trend you see. Explain.

The graph goes upward, because the price increases as the number of ears increases. The price is a function of the number of ears purchased.


As the number of ears of corn changed, the price a customer paid changed.

This is an example of two types of variables: those that lead the change; and those that change due to the leaders changing.

• independent variable - a variable that changes because something such as humans or time change it

usually graphed on the horizontal axiswill generally be x when we graph

• dependent variable - a variable that changes because the independent variable was changed

usually graphed on the vertical axiswill generally be y when we graph


EXAMPLE 1α: For a certain time, Lucinda jogs up a hill at a steady speed. Then she runs down the hill and picks up her speed.a. What happens to her speed when Lucinda jogs at a steady pace? When Lucinda runs down the hill?The speed remains the same when her jogging pace is steady. The speed increases when she runs downhill.

b. Identify the independent and dependent quantities.Time is the independent quantity, and speed is the dependent quantity.

c. Match the graph to the situation of Lucinda jogging. Which one fits best with the information we are given?

Graph 1

Speed

Time

Graph 3

Speed

Time

Graph 2

Speed

Time

This is it because it shows a steady speed for the uphill and an increased speed when going downhill.


A few last terms:

• relation - a set of ordered pairs

• domain - the set of first numbers from a set of ordered pairs

• range - the set of second numbers from a set of ordered pairs

The following is a relation.

The domain is in blue and the range is in red.

relation -> {(1, 2), (3, 5), (8, 4), (6, 2), (3, 1), (7, 4)}domain -> {1, 3, 8, 6, 3, 7} range -> {2, 5, 4, 2, 1, 4}

{1, 3, 6, 7, 8} To “spell” it right,

{1, 2, 4, 5} in order & no repeats.

chapter 01 – section 08 a preview of graphs and functions

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