SOLUTION: given the algebraic relation x=y^2+1, determine the domain, range, and whether or not it is a funtion. on my graphing calculator it shows a line that starts at (-.851,.386)to infin

Algebra ->  Algebra  -> Functions -> SOLUTION: given the algebraic relation x=y^2+1, determine the domain, range, and whether or not it is a funtion. on my graphing calculator it shows a line that starts at (-.851,.386)to infin      Log On

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Question 161526: given the algebraic relation x=y^2+1, determine the domain, range, and whether or not it is a funtion. on my graphing calculator it shows a line that starts at (-.851,.386)to infinity. it shows it as though if you did a vertical line test, it would be a function. I'm confused because if I insert a pos # into y or a - # into y, squaring it will give you the same number. you can't have 2 different y's giving the same x or it is not a function, right?
Answer by Edwin McCravy(6935) About Me  (Show Source):
You can put this solution on YOUR website!
given the algebraic relation x=y^2+1, determine the domain, range, and whether or not it is a funtion. 


I think you are a little confused. Before you enter it in 
your calculator you must solve the equation for y:

x=y%5E2%2B1
y%5E2%2B1=x
y%5E2=x-1
y=±sqrt%28x-1%29

This means the equation consists of two function graphs,

One function graph is the graph of this function, using
the positive square root:

y=sqrt%28x-1%29

drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0A%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28x-1%29%29+%29

The other function graph is the graph of this function,
using the negative square root:

y=-sqrt%28x-1%29

drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0A%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-sqrt%28x-1%29%29+%29

But the original equation

x=y%5E2%2B1

consiste of BOTH of these at the same time on the
same set of axes, like this:

drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28x-1%29%29+%2C%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-sqrt%28x-1%29%29+%29

and this is not a function because it does not
pass the vertical line test.  It is a parabola
that opens to the right.

Since the x-values of the graph start where x=1,
including that point, and the graph goes to 
infinity on the right the domain is matrix%281%2C5%2C%27%5B%27%2C1%2C%27%2C%27%2Cinfinity%2C%27%29%27%29

Since the y-values go both upward and downward
from 0 both to positive and negative infinity,
the range is   matrix%281%2C5%2C%27%28%27%2C-infinity%2C%27%2C%27%2Cinfinity%2C%27%29%27%29

No, it is not a function.

Edwin