Bell work: Which of these are ways to represent a function? f(x)=x+3 (0,1),(1,2),(2,3),(3,4),(4,5)… Double a number and add six The image to the right

What is a function? In your groups, arrive at a shared definition of what a ‘function’ is. When you’re finished, turn in your group’s definition(with all member’s names) We will discuss different definitions as a class.

1.1: Functions and Relations

Function, relation, or neither?

Function, relation, or neither?

Relations vs functions A relation is some relationship between inputs and outputs A function is a relation that matches each input WITH ONLY ONE output

Is this a function?

Which are not functions?

Domain and Range Domain is the set of all inputs(aka x-values) Range is the set of all outputs (aka y-values)

What is the domain and range of these functions? f(x) = 5x+7 g(x) = 5 𝑥 2 h(x) = 17 𝑥 2 −9 r(x) = 𝑥−100

1.2: Composition of Functions

What is a composition of functions?

Adding functions If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) + g(4) ? If h(x)= 𝑥 2 +𝑥+12, what is h(4) ?

Adding functions If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) + g(2) ? If h(x)= 𝑥 3 -2+ 𝑥−2 , what is h(2) ?

Subtracting functions If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) - g(4) ? If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) - g(2) ?

Multiplying functions If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) * g(4) ? If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) * g(2) ?

Dividing functions If f(x)= 𝑥 2 +5, and g(x) = x + 7, what is f(4) / g(4) ? If f(x)= 𝑥 3 -2, and g(x) = 𝑥−2 , what is f(2) / g(2) ?

IN GENERAL…what can we say about… f(x)+g(x)=… f(x)-g(x)=… f(x)*g(x)=… f(x)/g(x)=… (f+g)(x) (f-g)(x) (f*g)(x) (f/g)(x) As long as g(x) does not equal zero

If f(x) = 12x+5, what is f(3)? If f(x) = 12x+5, what is f(y)? Evaluating functions If f(x) = 12x+5, what is f(3)? If f(x) = 12x+5, what is f(y)? If f(x) = 12x+5, what is f( )?

If f(x) = 12x+5, what is f(3 𝑥 2 +7)? Evaluating functions If f(x) = 12x+5, what is f(3 𝑥 2 +7)?

Composition of functions The previous example was a composition of functions. Basically, everywhere we had a variable, we replace it with an entirely new function. This is denoted as 𝑓ᴑ𝑔(x), or as 𝑓(𝑔 𝑥 )

Find 𝑓ᴑ𝑔(x) for 𝑓 x =x+3, and g x = 𝑥 2 +7

Homework: Section 1.1, pages 9-11: 2, 10, 11, 13-15, 38-40, 42, 44, 47