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Presentation transcript:

Do Now: Grab a calculator Go to your Spring Board Book and rip out page 64 “Getting Ready for Unit 2” Also rip out pages 75-80 Start working on the problems

Unit 2: Linear Functions

Function Machine We have inputs and outputs.

Function Machine So when we put numbers in our functions (inputs), we have an answer come out (outputs) 5 2x+1 11

Domain… The domain is the set of all the number we can input The domain is the X-Values in a function

Domain… So in this case…the domain can be any number 2x+1

Range… The range is the set of all numbers we get for an output The range depends on the domain The range is the Y-Values in a function

Range… So in this case…the range depends on what numbers you input (domain) 2x+1

is there any number we could not put in for x? In our function is there any number we could not put in for x? No!

Because we could substitute any real number for x, we say the domain of the function is the set of real numbers.

Domain and Range in different forms Input Output 1 -2 2 3 4 7 Domain: Range:

Domain and Range in different forms

Domain and Range in different forms

Try These…

Finite vs. Infinite A Finite set has a fixed countable number of elements An Infinite set has an unlimited number of elements

Let’s look at this function machine x= 7 y = x = -2 y = x = .5 y =

x= -5 y = x = .6 y = x = -10 y =

Sometimes the function itself limits the domain or range. In this function, can x be any real number?

Then we would have to divide by 0. What would happen if x were 3? Then we would have to divide by 0. We can never divide by 0.

The most common rules of algebra that limit the domain of functions are: Rule 1: You can’t divide by 0. Rule 2: You can’t take the square root of a negative number.

Page 75 in Spring Board Notes