Introduction To Functions

Introduction to Functions. What goes in must come out. Fill in the blank:

–

A _________________ is a relationship between two quantities called input and output.

–

The collection of all ___________________ values is called the domain of the function. ○

–

The input is often represented by _____

The collection of all ___________________ values is called the range of the function. ○

The output is often represented by _____

–

In a function, there is exactly one ___________ for each ______________.

–

An _____________________________________ is a table that list the outputs for several different inputs.

–

There are 4 ways to represent a function they are with ______________________________________________________.

Homework sheet of paper

Do all work on a separate Bring it to Mr. Woodson to have him check it.

Introductory List the tables below that or are not. (List at least 3 a) Inp Outp b Inp ut ut ) ut 1 1 2 3 1 2 5 5 4 2 8 4

are functions and those that are not functions. on each) Outp c Inp Outp d Inp Outp e Inp ut ) ut ut ) ut ut ) ut 1 2 5 5 0 3 2 4 6 4 0 4 3 6 5 3 0 5 4 8 6 2 0 6

g)

Inp Outp h Inp Outp i Inp Outp j Inp ut ut ) ut ut ) ut ut ) ut 4 7 1 1 2 10 1 2 3 0 0 4 12 2 1 1 5 5 6 10 2 4 7 2 2 8 12 3 Make an input-output table of the function. Use 0,1,2, & 3 1) y = x 2) y = x + 39 3) y = 21 – x 6) y = 3x = 4x + 12

7) y = 9 – x

8) y = x + 5

Outp k Inp ut ) ut 1 12 2 14 3 16 4 18 as the domain. 4) y = 4x

Explain why they are Outp ut 6 5 4 3

f )

Inp ut 4 13 9 4

Outp ut 3 7 4 0

Outp l ut ) 10 12 10 12 (Do 3)

Inp ut 11 9 10 9

Outp ut 0 1 1 0

9) y = 10 – 3x

5) y = 2x + 3 10) y

Intermediate Make an input-output table of the functions. Use 2,2.5,3,5.5,&6 as the domain. (Do 3) 11) y = 22x + 7 12) y = x2 – 2.5 13) y = 4x + 1.5 14) y = 24 - x.5 2 15) y = 2x + 3 16) y = 3x + 1.5 17) y =x2 + 2.5 18) y = x + 53 19) y = 3 - x22 2 20) y = x + 12 Decide whether y is a function of x in the situation. Justify your answer. (Do 2) 21) The amount of sales tax y on a purchase of x dollars in a specific store. 22) The temperature y after a change of 10˚ from temperature x. 23) The number of days y in a year x. 24) The yards gained y on down x

Mastery Make an input-output table of the functions. Use 1, 1.25, 2.35, 2.8, & 3 as the domain. (Do 2) 25) y = 7x – 2.1 26) y = x5 + 9.2 27) y = x2 - .7 28) y = (x-0.4)22 Look for a pattern and write an equation for the function defined by the input-output table. (Do 2) 29 Input Output 30 Inpu Outp 32 Input Outp

)

) t 2 7 5 0 3 3 1 5 6 5 13 2 Last One 33) Give an example of a function that has

ut 1 7 -2 10

) 2 3 4 6

ut 6 4 3 2

many values in the domain and only one element in the range.