Fun with Functions Katherine Doan

9/22/10

The Problem

Darby is saving money for her prom dress. If every yard of fabric costs $6.85, how much money will it cost to buy at least 12 yards of fabric?

The Equation

My equation is:

y= 6.85x or f(x)= 6.85x

X= the number of yards of fabric she buys

Y= the total cost of the fabric

The Domain and Range

Domain – the x values

◦My domain is x≥12

Range – the y values

◦My range is y≥82.2

Independent and Dependent

The total cost of the fabric depends on the number of yards of fabric she buys.

Because:◦The independent variable is x which is the

number of yards of fabric she buys.◦The dependent variable is y which is the total

cost of all the fabric.◦y depends on x

Function or Not?

You can tell if a relation is a

function if every y value has a

different x value.Since all of the x values are

different, it is a function.

Table of Values

x 6.85x y (x,y) 12 6.85(12) 82.2 (12, 82.2)

13 6.85(13) 89.05 (13, 89.05)

14 6.85(14) 95.9 (14, 95.9)

15 6.85(15) 102.75 (15, 102.75)

16 6.85(16) 109.6 (16, 109.6)

Prom Dress Graph

The total number of yards of fabric Darby buys determines the total cost of the fabric. If she buys 12 yards of fabric it will cost $82.20, but if she buys 16 yards of fabric it will cost $109.60. As the number of yards she buys goes up, the price goes up.

11.5 12 12.5 13 13.5 14 14.5 15 15.5 16 16.50

20

40

60

80

100

120

Number of yards of fabric

Tota

l co

st (

dolla

rs)

Continuous & Discreet

My graphed data is continuous.

It is continuous because you can

purchase one yard, two yards or any

number in between. You can have

any points in between one and two.

In Conclusion:

Darby will have to spend at least $82.20 on her dress in order to have the minimum amount of fabric to make a dress. If she wants to add a longer skirt or a sleeve she will need more fabric. I sure hope she can save up all that money in time!