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