SOLUTION: Which of the following does not express y as a function of x? A. y = |x − 3|; B. y = −3; C. x = y; D. x = y^2 + 4; E. none

Algebra ->  Functions -> SOLUTION: Which of the following does not express y as a function of x? A. y = |x − 3|; B. y = −3; C. x = y; D. x = y^2 + 4; E. none      Log On


   

Question 240654: Which of the following does not express y as a function of x?
A. y = |x − 3|; B. y = −3; C. x = y; D. x = y^2 + 4; E. none
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
An equation which expresses y as a function of x is an equation which can be solved for y. This means we can get y by itself on one side:
y = single-valued-expression (without-y's)

Since the first three equations are already in this form, they express y as a function of x. So the only possible answers are (D) or (E). Let's try to solve (D) for y:
x+=+y%5E2+%2B+4
Subtract 4 from each side:
x-4+=+y%5E2
In order to eliminate the exponent we find the square root of each side:
sqrt%28x-4%29+=+sqrt%28y%5E2%29
In simplifying the right side, a common error is to forget to use absolute value. sqrt%28y%5E2%29 is not just "y". It is abs%28y%29. So the equation simplifies to:
sqrt%28x-4%29+=+abs%28y%29
And solving an absolute value equation requires two equations:
sqrt%28x-4%29+=+y or -sqrt%28x-4%29+=+y
Often some of these steps are skipped and a jump is made from
sqrt%28x-4%29+=+sqrt%28y%5E2%29
to the shorthand (abbreviation) for the pair of equations:
0+%2B-+sqrt%28x-4%29+=+y (Excuse the extra 0. Algebra.com's formula software can't do "plus-or-minus" without something in front of it.)

Whether we use the two separate equations or the shorthand, we are not able to express y as a "single-valued" function of x. So the answer is (D).
An alternate way to solve this kind of problem is to use graphs. If you are good at graphing you can use the vertical line test to see if y is a function of x. (D) works out to be a parabola that opens to the right. If you can picture this you will realize that it fails the vertical line test. (The others all pass.)