functions for shs demo jaydes

INTRODUCTION tO

FUNCTIONSPrepared by: JAYDES ADLAO TAPERLA

SHS APPLICANTjay1577t@yahoo.com

d.appreciate the importance of learning the functions.

Objectives: a.define functions;b. identify the domain and range of functions; c.solve problems involving functions; and

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• functions• independent variable• input• output• domain• range• relation

• Functions- is a rule that for every input assigns a specific output.

Definition of terms

Relation - is any set of ordered pairs. The first set , called the domain,

and second set, is called the range, such that each element in the domain

corresponds to exactly one element in the range.

the input , usually x, is called independent variable.

the output , usually y, is called dependent variable.

you can also think of a function as machine in which each input produce output

Let's say you own a prepaid phone. Your monthly cost is a function of the number of minutes you used. The cost is P3.00 pesos per minute.

Example:

Function machine

multiplied by P 3.0010mins. 30.00

20 mins. 60.00

x= the number of minutesy= the monthly costy= 3xf(x)= 3x

f(10)=30.00 (10,30)f(20)=60.00 (20,60)

Example 2:Let's say you pay P175.00 per month for your digital cable television. Your cable company offers pay per view movies for P45.00 per movie.Write a function that models the total costs of your cable bill.

P175.00

fixed cost variable cost

movies watched

times P45.00

number of movies watched

total monthly cost

x= the number of movies watched

y= total monthly costs

y= 175 + 45x

f(x) =175 + 45x

f(2)= 175 + 45(2) = 265f(2)= 265

The set of all possible inputs is called DOMAIN.

The DOMAIN is the set of all possible x-values.

The set of all possible outputs is called RANGE.

The RANGE is the set of all possible y-values.

Determine the domain and range.

The cost of the taxi is P40.00 flag fee plus P3.00 per kilometers.

x= the number of kilometersy= the total costs y= 40+3x

f(x)= 40+3xDOMAIN:x ≥ 0

notice we used "x" since x represents

the DOMAIN

RANGE: y

≥ 40

notice we used "y" since y represents

the RANGE

3.What best describe, when there is an input, there is an output?

1. What do you mean by domain? What is range?

2. On the given illustration, What next if you have an input?

1. How do you find this learning?

Group I &II. The basic charge is P15.00 per cubic meter and the other charges amount to P40.00, and x is the amount of water consume.

Solve for the needed value and write a function that models the situation.Determine the domain and range

Group III & IV. The daily wage of a sales lady is P280.00 and the over time payment of P20.00 per hour.

Group activity

Rubrics for assessment

4 points The answer is clear & complete, The explanation includes a mathematically correct- reason.

3 points The answer is correct; the explanation lacks clarity

2 pointsThe explanation lacks clarity or incomplete but indicate indictae some connect & relevant reasoning.

1points The explanation, if any uses irrelevant argument.

Individual output (1/2 crosswise)

An open box is to be made from a rectangular piece of tin 12 inches long and 10 inches wide by cutting pieces of x-inch square from each corner and bendin

g up the sides.a. Find a formula that expresses the volume V of box as a function of x

b. What is the volume if 3-inch square is cut out?

ASSIGNMENT: same group earlier:

The mind is like a parachute.

It functions best when open.

Thank You!

Prepared by:

JAYDES A. TAPERLA