Warm-Up #1 1/25/2013Keep all warm-ups on one piece of notebook paper If you run out of room, use another piece.Label and date all warm-ups.They may be taken up at any time for a quiz grade.

1. The following data set represents the height of a ball over a period of distance, in feet. Determine whether a linear or quadratic equation would be the best fit. Find this equation and explain why.

2. The expression 2π(rh + r2) represents the total surface area of a cylinder with height h and radius r. What is the surface area of a cylinder with height 5 centimeters and radius 2 centimeters? Leave your answer in terms of pi.

Distance, x 20 40 60 80 100 120 140 160 180 200

Height, h 25 40 55 65 71 77 77 75 71 64

Domain: the set of all inputs (x-values) in a relation.

Domain: the set of all inputs (x-values) in a relation.

Range: the set of all outputs (y-values) in a relation.

Range: the set of all outputs (y-values) in a relation.

5 x2 25

How would you use your calculator to solve 52?

The number you entered is the input number (or x-value on a graph).The result is the output number (or y-value on a graph).

InputInput OutputOutput

A function is a relation in which each of its inputs (x-values) provides exactly one

output (y-value).

A function is a relation in which each of its inputs (x-values) provides exactly one

output (y-value).

There are many ways to represent relations:There are many ways to represent relations:

A relation is a set of data with no restriction on input-to-output values.

A relation is a set of data with no restriction on input-to-output values.

These are all ways of showing a relationship between two

variables.

These are all ways of showing a relationship between two

variables.

GraphEquationTable of valuesA set of ordered pairsMapping

Function

X values are always located on the right and y values are

on the left.

They can be represented bywords, symbols or numbers.

Function

X values are always located on the right and y values are

on the left.

They can be represented bywords, symbols or numbers.

This represents a function as every input value (x) has only been used once.

This represents a function as every input value (x) has only been used once.

A Relation is a set of data with no restriction on input-to-output values

(x and y values may be repeated).

This represents only a relationbecause the input value or x-value of 2 was used twice.

Therefore this relation is not aFunction.

A Relation is a set of data with no restriction on input-to-output values

(x and y values may be repeated).

This represents only a relationbecause the input value or x-value of 2 was used twice.

Therefore this relation is not aFunction.

All functions are relations but not all relations are functions!

All functions are relations but not all relations are functions!

a)

b)

a)

b)

)}8,3(),1,1(),0,0(),4,2(),9,3{(

20 Hours

25 Hours

30 Hours

40 Hours

$200

$425

$350

$450Time (in seconds)

Height of Skydiver (in feet)

0 10000

4 9744

8 8976

12 7696

16 5904

Vertical Line Test: if every vertical line you can draw goes through only 1 point then the relation is a function.

Vertical Line Test: if every vertical line you can draw goes through only 1 point then the relation is a function.