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Question 54567This question is from textbook elementary and intermediate algebra
: Im not understanding this function stuff. Can someone please explain it to me. Here is an example problem. y^2=x+1 I know that you enter a number into one of the variables and solve for the other variable, but Im not sure what makes a problem like this functional or non functional.
This question is from textbook elementary and intermediate algebra
Found 2 solutions by venugopalramana, Edwin McCravy:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Im not understanding this function stuff. Can someone please explain it to me. Here is an example problem. y^2=x+1 I know that you enter a number into one of the variables and solve for the other variable, but Im not sure what makes a problem like this functional or non functional.
IF YOU KNOW SUBSTITUTION OF VALUES FOR X AND FINDING Y ,THEN IT IS SIMPLE
TEST WHETHER YOU GET A UNIQUE OR MULTIPLE VALUES FOR Y FOR A PARTICULAR VALUE OF X...IF YOU GET UNIQUE VALUE THEN IT IS A FUNCTION .OTHERWISE IT IS NOT.
IN GENERAL IF Y1 IS NOT EQUAL TO Y2 THEN X1 SHOULD NOT BE EQUAL TO X2 FOR IT TO BE A FUNCTION .OTHERWISE NOT.NOTE THAT IT DOES NOT MATTER THE OTHERWAY AROUND..THAT IS X1 AND X2 CAN HAVE SAME Y VALUE ..THAT IS EVEN IF Y1=Y2, X1 MAY NOT BE EQUAL TO X2.
SEE FOLLOWING EXAMPLES
EX.1... Y = X+2...WE KNOW FOR CERTAIN HERE THAT IF Y1 IS NOT EQUAL TO Y2,X1 WILL NOT BE EQUAL TO X2..HENCE ITIS A FUNCTION
EX.2... Y=X^2...HERE ALSO IF Y1 IS NOT EQUAL TO Y2..THEN X1 WILL NOT BE EQUAL O X2.SO IT IS A FUNCTION.SEE THAT HERE X1=+2 AND X2=-2 HAVE SAME Y VALUE +4..IT IS OK FOR A FUNCTION.THE OTHER WAY ROUND IS NOT ALLOWED.
EX.3.....Y = + OR - SQUARE ROOT OF (X)...THIS IS NOT A FUNCTION.SINCE
X =4 GIVES RAISE TO 2 DIFFERENT VALUES OF Y NAMELY +2 AND -2...IT IS NOT UNIQUE.HENCE THIS IS NOT A FUNCTION.
NOW I THINK YOU CAN ANSWER YOUR PROBLEM WITH THIS TEST AND EXAMPLES
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! Im not understanding this function stuff.
Can someone please explain it to me. Here
is an example problem. y^2=x+1 I know that
you enter a number into one of the variables
and solve for the other variable, but Im not
sure what makes a problem like this functional
or non functional.
Just solve
y² = x+1
for y.
When you take square roots of both
sides, you must include
+ and -. So
___
y = ±Öx+1
So for every value of x, (other than x = -1
which gives only y = 0), there are two y-values.
For example when x = 0, then y = ±1. That is,
we get two y-values, both 1 and -1, for only one
x-value, 0. This is what must never be
true of a function. So therefore y² = x+1
DOES NOT represent a function. The
graph of y² = x+1 looks like this:
But the graph of a function must never pass over
or under any part of itself.
Edwin McCravy
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