Functions A Brief Overview of What We Already

Functions A Brief Overview of What We Already Know Before We Leap into Something New : )

Functions… /We explored functions with The Raven and the Jug /But, what the heck are they?

Think about this… /You get your first job and your friends ask you: “How much money will you earn by the end of the year? ” /Well, it all depends on the time you work

Think about this… /With your new job comes the responsibility of paying your own cell phone bill. You might wonder: How much will it cost? /Again, it all depends on how many minutes you use and how many texts you send

Think about this… /The outcome of those two events will vary because other factors that affect them vary /*Main Idea* Relationships in which the outcome depends on certain inputs are called functions

Have you ever heard someone say… /“Your success is a function of your effort. ” ? ? Or “True friendship is a function of time. ” ? ? The expression “…is a function of…” can be used to show a dependent relationship between two variables. /So if success is a function of effort, your success depends on your effort /And if friendship is a function of time, friendship depends on time. /And…if y is a function of x, then the value of y depends on the value of x as in y = 2 x + 1 /

Functions /Functional relationships are dependent relationships, meaning: the output (the result) depends on the input. / Example: Your salary depends on the number of hours worked output input

Input-->Output /The input of a function is called the independent variable and is represented by x /The output of a function is called the dependent variable and is represented by y

State which one is input/independent/x and which one is output/dependent/y /My test scores and how much I study. /The amount deposited in the bank and the interest earned. /The water level and number of marbles placed in the water

But what do functions look like? /Functions can be words or situations /Functions can be a graph /Functions can be an equation /Functions can be a table or chart /Functions can be an ordered pair

Remember… -We used functions yesterday on shodor. com and we used functions on our homework last night -Functions are just a rule for how we get from the input to the output X(input)|Y=2 x + 1(rule/function)|Y(output) 0 | y = 2(0) + 1 | 1 1 | y = 2(1) + 1 | 3 2 | y = 2(2) + 1 | 5

From Functions to Linear Functions /Functions are a rule in which one variable depends on another /Linear functions are a specific type of function /Linear functions relate two variables to one another proportionately /In other words, linear relations have a constant rate of change (like how the water level rose at a constant rate in our lab)