How can I tell if an algebraic equation is a function?

Question

How can I tell if an algebraic equation is a function?

Answer 1

If it is one-to-one then it will be a fucntion.

one-to-one  means for any input the output should be unique.

like if we consider the equation f(x) = x+3

for any value of x (input) there will be only one (unique) value of f(x) which is the output.

but in f(x) = sqrt x , where xis an integer. is not a function

because for x=25, there will be two f(x) +5 and -5. which means there is more than one output.

Edit: Nottheja..sir you are right... I got it now.

Answer 2

If 2 different x values give the same y value it is not a function; otherwise it is.

Answer 3

Careful: if the same x can give you two different y values, it is not a function.

Some things to look for that make it not a function:

| y |, y^2, +/- x

in a function, x can not be repeated

so you can't have both (1,2) and (1,-3) in a function

you can't have both (4,2) and (4,-2) in a function (which would come from x = y^2, or y = +/- sqrt(x)

you CAN have (4,16) and (-4, 16) (two different x-values giving the same y-value)

EDIT: careful, Jaya... a function can be a function without being 1-1 (not repeating either x or y values)

y-values can be repeated in a function, but x-values cannot

in otherwords: your letter grade is a function of your numerical score (if you get a 94 in math, that will be an A)

but your numerical score is not a function of the letter grade (if you get an A in math, you don't know your average for sure-- it could be a 93 or 94 or 95 or 94.5 or.....)

y = sqrt(x) is a function

sqrt(25) = 5 (and only 5, the principal root)

this is different than solving y^2 = x

then if x = 25, you could be either 5 or -5