1. ## Functions

I've been stuck on this problem for a while and it seems simple yet i'm having trouble help

x + 1 = Absolute Value of Y

Is this a function? If so why? If not why? Thanks in advance

2. Originally Posted by JonathanEyoon
I've been stuck on this problem for a while and it seems simple yet i'm having trouble help

x + 1 = Absolute Value of Y

Is this a function? If so why? If not why? Thanks in advance
Hint: did you graph it? do you know how? recall the definition of a function (and think "vertical line test")

what do you come up with?

3. Originally Posted by Jhevon
Hint: did you graph it? do you know how?

Well so far i've assumed that

x + 1 = absolute value of Y

is the same as

absolute value of (x + 1) = y

In this case, the graph should be a triangle where the vertex is (-1,0) and thus IS a function seeing as no single x value is having two different y values. Am I right?

4. Originally Posted by JonathanEyoon
Well so far i've assumed that

x + 1 = absolute value of Y

is the same as

absolute value of (x + 1) = y

In this case, the graph should be a triangle where the vertex is (-1,0) and thus IS a function seeing as no single x value is having two different y values. Am I right?
that's wrong i'm afraid.

recall, absolute values always give positive outputs, but what is inside the absolute values could be negative. since we have |y| = something, it means the y can be positive or negative, thus we have:

$|y| = x + 1 \implies y =\left\{\begin{array}{cc}x + 1,&\mbox{ for }
x\geq -1\\-(x + 1), & \mbox{ for } x \geq -1\end{array}\right.$

x + 1 must be non-negative in any case, that's why we must always have that x is greater than or equal to -1

Now what do you think?

5. Originally Posted by Jhevon
that's wrong i'm afraid.

recall, absolute values always give positive outputs, but what is inside the absolute values could be negative. since we have |y| = something, it means the y can be positive or negative, thus we have:

$|y| = x + 1 \implies y =\left\{\begin{array}{cc}x + 1,&\mbox{ for }
x\geq -1\\-(x + 1), & \mbox{ for } x \geq -1\end{array}\right.$

x + 1 must be non-negative in any case, that's why we must always have that x is greater than or equal to -1

Now what do you think?

Haha I originally thought about it this way with restrictions on the x value due to the absolute value of y. MMmM i'm right back to where I was again help

6. Originally Posted by JonathanEyoon
Haha I originally thought about it this way with restrictions on the x value due to the absolute value of y. MMmM i'm right back to where I was again help
what does the vertical line test tell us?

7. Originally Posted by Jhevon
what does the vertical line test tell us?

If a vertical line intersects a line on a graph at more than two points, it is not a function.

8. Originally Posted by JonathanEyoon
If a vertical line intersects a line on a graph at more than two points, it is not a function.
actually, it's if it cuts it more than once. why is that? a function is a relation in which each element in the domain (the set of inputs) maps to one and ONLY one element in the range (the set of outputs).

if we have a relation with x-values as the inputs, in which a vertical line cuts the graph of the relation at more than one point, it means there is some input (x-value) that has more than one output (y-value) and is therefore not a function.

look at the graph that we have for this problem (see below).

note that any vertical line drawn of the form x = c, where c is a constant greater than -1, will cut the graph twice. thus this is NOT a function, since it fails the vertical line test

alternatively, we could say that the x-value, x = 0 (for example) maps to two y-values, (y = 1, and y = -1) thus we have a one-to-many relation which is not a function (functions are one-to-one or many-to-one relations)

9. Originally Posted by Jhevon
actually, it's if it cuts it more than once. why is that? a function is a relation in which each element in the domain (the set of inputs) maps to one and ONLY one element in the range (the set of outputs).

if we have a relation with x-values as the inputs, in which a vertical line cuts the graph of the relation at more than one point, it means there is some input (x-value) that has more than one output (y-value) and is therefore not a function.

look at the graph that we have for this problem (see below).

note that any vertical line drawn of the form x = c, where c is a constant greater than -1, will cut the graph twice. thus this is NOT a function, since it fails the vertical line test

alternatively, we could say that the x-value, x = 0 (for example) maps to two y-values, (y = 1, and y = -1) thus we have a one-to-many relation which is not a function (functions are one-to-one or many-to-one relations)

thanks alot! this really cleared alot up for me. I had forgotten that in an absolute variable equation, both postive and negative values of the number must be accounted for. For instance, for the x-value 1, I was just using 2 = absolute value of Y instead of both 2 and -2. Thanks Jhevon~!

10. Originally Posted by JonathanEyoon
thanks alot! this really cleared alot up for me. I had forgotten that in an absolute variable equation, both postive and negative values of the number must be accounted for. For instance, for the x-value 1, I was just using 2 = absolute value of Y instead of both 2 and -2. Thanks Jhevon~!
you're welcome. and it is y = 2 or -2, |y| = |2| or |-2| = 2

but i think you got the idea