INTRODUCTION TO FUNCTION NOTATION Use your device/brain to define these two terms: Independent Variable Dependent Variable

Definitions (1) Independent Variable – it stands alone, represents the input of values, is the x part of y = x. A good example is the age of a person as it is NOT affected by other variables. (2) Dependent Variable – it is affected by another variable, represents the output of values is the y part of y = x. An example is your grade in this class.

TWO EXAMPLES For the pair below, decide which is the independent variable and which is the dependent variable. (1) time and amount of sales tax collected Time would be independent here and amount of sales tax collected would be dependent. (2) heart rate and stress Heart rate would be dependent and stress would be independent.

Which is Which??????????? For the pairs below, decide which is the independent variable and which is the dependent variable. Explain. (1) spring rainfall and wildflowers (2) number of wild rabbits and available food supply (3) number of predators and number of rabbits (4) amount of money spent and articles of clothing bought (5) amount of stagnant water and number of mosquito larva

ANSWERS (1) spring rainfall and wildflowers Independent = spring rainfall (2) number of wild rabbits and available food supply Independent = available food supply (3) number of predators and number of rabbits Independent = could be either (4) amount of money spent and articles of clothing bought Independent = articles of clothing bought (5) amount of stagnant water and number of mosquito larva Independent = amount of stagnant water

GROUP WORK With your group, come up with three more examples and we will work a few shortly.

FUNCTION NOTATION https://www.youtube.com/watch?v=Kj3Aqov52TY Watch this short clip:

FUNCTION NOTATION W(r) = r Dependent = Independent So y = x Or f(x) = x Or Wildflowers = Spring Rainfall W(r) = r where w = number of wildflowers and r = amount of rainfall

FUNCTION NOTATION Write a sentence based on the variables. W(r) = r w = wildflowers and r = rainfall Write a sentence based on the variables. The number of wildflowers is dependent on the amount of rainfall. The number of wildflowers is a function of the amount of spring rainfall.

Function Notation Example Lets consider the variables weight and exercise: Which is dependent? I say weight depends on exercise or weight is a function of exercise. So weight = exercise So w(e) = e

GROUP WORK For each pair of variables, (1)write a sentence based on which variable is dependent on the other (2)write your sentence into function notation

FUNCTION NOTATION (1) electric bill and kilowatt hours (2) river level and amount of rainfall (3) area and diameter (4) cd’s bought and money spent (5) time of day and temperature

ANSWERS electric bill and kilowatt hours B(k) = k (2) river level and amount of rainfall L(r) = r (3) diameter and area A(d) = d (4) cd’s bought and money spent M(n) = n (5) temperature and time of day T(t) = t