Question

Is (y+1)^2 - 3 = 2x a function? If so, what is its domain and range? Also how do I know it's a function and its domain and range?

Answer 1

Consider the following:\[(y+1)^2 - 3 = 2x \rightarrow (y+1)^2 = 2x+ 3\rightarrow y=\pm \sqrt{2x+3}-1\]This says, for any given x, there are usually two values of y.

A function is a correspondence between two sets (the domain and the range) such that for every element in the domain, there is exactly one corresponding element in the range. Said a little less formally, for every x, there is exactly one y.

This relation does not meet the required specification, so is not a function.

Answer 2

oh.. so wait, when you said for any given x there are suually two values of y, what do you mean?

Answer 3

Look at the end of the sequence of equations. y=plus or minus a function of x. If y is either plus or minus, it has two values.

Answer 4

ohhh, i see. Alright, thank you!!

Answer 5

My pleasure.