AA Section 1-2

transcript

SECTION 1-2What Is a Function?

Warm-upTo determine the retail price a of the androids that Matt

Mitarnowski sells, he multiplies the wholesale price p by 1.75. Write an equation showing the situation and make a table

showing 6 values.

a = 1.75p

showing 6 values.

a = 1.75p

p $1.00 $2.00 $3.25 $17.32 $8.00 $9.14

a $1.75 $3.50 $5.69 $30.31 $14.00 $16.00

Dependent Variable:

Dependent Variable: The value that depends on another variable

Independent Variable:

Independent Variable: The variable that determines the dependent variable; relies on nothing

Question:

Question: Why do we call them dependent and independent variables?

Function:

Function: A pairing between two variables so that the independent variable matches with only one dependent variable.

“Is a function of ”:

“Is a function of ”: Statement used when we have a function

[Dependent variable] is a function of [independent variable]

Example 1The table below shows the average temperature T in Fahrenheit

for each month M in Annville, PA.

M Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

T 35 39 49 61 71 79 83 81 73 63 51 40Source: http://www.weather.com/outlook/travel/vacationplanner/vacationclimatology/monthly/USPA0042

a. Is T a function of M? b. Is M a function of T?

Yes, each month has only one average temperature

Yes, each temperature is listed for only one month

Domain:

Domain: Anything that can possibly be substituted in for the independent variable

D = { }

Range:

D = { }

Range: Any value that can be listed as the dependent variable

D = { }

R = { }

D = { }

R = { }

Input:

D = { }

R = { }

Input: Another word for the independent variable

D = { }

R = { }

Output:

D = { }

R = { }

Output: Another word for the dependent variable

Example 2Give the domain and range of example 1.

T 35 39 49 61 71 79 83 81 73 63 51 40

D = {Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec}

T 35 39 49 61 71 79 83 81 73 63 51 40

D = {Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec}

R = {35, 39, 40, 49, 51, 61, 63, 71, 73, 79, 81, 83}

And now for some sets

Natural Numbers:

Natural Numbers: ℕ = {1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

ℕ = {1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

Integers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

Integers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

Integers:

Rational Numbers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

Integers:

Rational Numbers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}

ℚ; the set of numbers that can be written as a ratio

Natural Numbers:

Whole Numbers:

Integers:

Rational Numbers:

Real Numbers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Natural Numbers:

Whole Numbers:

Integers:

Rational Numbers:

Real Numbers:

ℕ = {1, 2, 3, ...}

{0, 1, 2, 3, ...}

ℤ = {..., -3, -2, -1, 0, 1, 2, 3, ...}

ℝ; any number that can be written as a decimal

Homework

p. 15 #1-23

AA Section 1-2

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