we will discuss independent and

dependent variables recall that a function is when one input of a relation

is linked to only one output of the relation meaning a function has only one

output for one input we represent functions by replacing the y with f of X

f of X equal to Y say F is a function of X so when we write f of X we are really

saying that F is a function of X now what do we mean by this well we call f of X or Y the dependent

variable and the reason why is because this value Y or f of X is dependent on

the value of x. X is the independent variable so whatever variable is inside

the parenthesis of your function is the independent variable in the entire

function would be the dependent variable so let’s look at a few examples what is

the independent and dependent variable f of X equal to three halves x + 1

notice that X is the variable in parenthesis therefore X is the independent variable

and f of X the entire function is the dependent variable not too bad it doesn’t necessarily

always have to be f or x like an example B we have h of t we noticed t is

the variable in the parenthesis therefore T is the independent variable

and the entire function H of T is the dependent variable so notice the first two examples x

inside the parentheses is the independent variable T an example B is

the independent variable so looking at example c) we can see that r is the

independent variable and the entire function G of r is the dependent

variable and looking at the last one which is a little interesting because we

didn’t put the left side in function notation we left it as y equal to square

root of n minus 16 but since on the right side we have the variable n inside

the equation with some other operations this implies that n is the independent

variable and Y is the dependent variable but why would this be important well let’s look at a few more examples

that give a little more meaning to the idea of the independent dependent

variable and these examples we want to identify the independent and dependent

variable but also what each one represents so in the first example it talks about

the cost where x is the number of miles driven

and C of X is the cost for driving the car for a day well right away notice that X is the

variable in parenthesis so X is the independent variable and the entire

function C of X is the dependent variable and the next question asks what

does each variable represent so X maybe the independent variable but

there’s units attached x is the number of miles driven and C of X is the cost

of renting a car for a day alright so let’s look at the

others a rocket is launched at T equals 0 seconds its height in feet above sea

level as a function of time is given by H of T is negative 16t squared plus 96t Plus 256 so right away looking at the function we

see that t is the independent variable and H of T is the dependent variable but

what it does each represent well if T is the independent variable it represents time in seconds and H of T represents the height above sea level what about the next one and the profit

for a certain commodity n where n is in units is given by the function P of n

equals negative 25 n squared plus 425 n + 1500 we can see that and is the

independent variable and P of n is the dependent variable but what each

represent well n is the number of units of the commodity and P of n is the

Profit looking at the last example the revenue R of x of producing and selling X awesome hearing aids is modeled by the function r of x equals negative

6x squared plus 67x so right away we can see that X is the independent variable and R of x is the

dependent variable but what does each represent well x is the number of

Awesome hearing aids and R of X is the revenue