 # Independent and Dependent Variables

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