State the domain, range and tell whether or not it is a function. Algebra 1 Warm Up State the domain, range and tell whether or not it is a function. {(3,2), (4,5), (6,7), (8,9)} 2. {(-3,2), (-4,-3), (8,2), (8,1)} 3. What is a function?

Warm-Up Answers: Domain {3,4,6,8} Range {2,5,7,9} yes it is a function Domain {-4,-3,8} Range {1,2,-3} This is not a function because a value in the domain is repeated A relationship in which no two ordered pairs have the same 1st coordinate, and a different 2nd coordinate. In other words x cannot be repeated and have two different y values

Function Notation and Function Notation with Graphs Lesson 9.5 Function Notation and Function Notation with Graphs

Remember…. A Function is: a rule that establishes a relationship between two quantities (input-output). AND…..For each input, there is exactly one output! So, X VALUES CANNOT REPEAT!

What is function notation? Functions are written using f(x) notation it is read “f of x”. It is one variable, it is like the y. Do not separate them. What does that mean? f(x) is the same as y We can use g(x) and h(x) as well as others but these are the most common.

Function Notation Practice Use the following functions f(x) = 3x+x2 and g(x) = -5x - 2 Example 1: Find f(2) _________________ _________________ Hint: Go to your function and everywhere you see an x, plug in a 2 = 3(2) +22 f(2) = 6+4 f(2) = 10 Then simplify – remember your order of operations! So f(2) = 10 means the function value at 2 is 10

Try these on your own, use f(x) = 3x+x2 and g(x) = -5x - 2 Example 2: g(-2) = Example 3: f(-3) = Example 4: f(1) + g(2) = 8 -8

Okay, let’s try a harder one! Using the following functions f(x) = 3x+x2 and g(x) = -5x - 2 Find f(a) But it is another variable!!!! Don’t worry, just follow the same rule replace (substitute) “a” every where you see “x” f(a) = 3(a) + a2

Use the following function Your Turn… Use the following function g(x) = -5x – 2 Example 5: g(b) Example 6: g(z - 1) Example 7: g() -5b - 2 -5z + 3 -5 - 2 Don’t forget to simplify when you can!

So Function notation says: That f(x) (or g(x), h(x), z(x), b(x)…you get the idea) is just another way of writing y = You also know we can evaluate these equations for certain values, like f(2) or g(c + 4).

The key is, whatever is in the parentheses…you plug it in every single time you see a variable in the original equation. It doesn’t matter if it is a number, variable, expression, or symbol…when you see the variable, you Glade it! (Plug it in, plug it in!)

Practice with some tougher problems… Evaluate f(x) = -3x + 2 for f(a + b) Answer: f(a + b) = -3a – 3b + 2 Evaluate g(x) = 4x + 13 for g(3x + 2) Answer: g(3x + 2) = 12x + 21

What about combining two different functions? Using f(x) = 2x2 + 3 and g(x) = 5x - 1 Find: f(-2) + g(4) 2. f(3)*g(-5) Answers: 1. f(-2) + g(4) = 30 2. f(3)*g(-5) = -546

Now let’s look at function notation and graphs We can use a graph to find a function value, which we can then use to evaluate without even having an equation! Cool huh?! Let’s take a look…

Using the following graph find… f(x) -2 f(2)=________ f(4) +5 = _________ find x when f(x)=-3 ___ 0+5=5 1 Note: the first 2 problems we knew the x-value on the graph and from that found the y-value (the output), but on the last problem we were given the function value (the y) and we found the x!

Using the following graph find… g(x) Notation Value g(-3) g(0) + g(5) g(4) ÷ g(3) g(1) – g(-4) 3 -1 + (-1) = -2 -3 ÷ 1 = -3 -2 – 1 = -3

Summary: In your own words explain how graphs are a useful way to evaluate equations without being given the actual equation. Homework: Worksheet 9.5