How do I determine whether y is a function of x; y - 2x^2 = 14 ???

Question

:)

Answer 1

Does y depend on x? That is, if I tell you x, can you find y? Here you can because you can rearrange the function to be

y = 2x^2 + 14

so if I tell you what x is, you can tell me what y is. So yep -- it's a function of x.

Answer 2

ok, so y is a function of x if it can be written in y= something form, and if it passes the vertical line test
It passes the vertical line test and is a function if there is nowhere on the graph where you can draw a line and have it go through two points on the graph (a circle, for example, would NOT pass the vertical line test, and is not a function of x)

so now, you have y-x^2 = 14
so you want to try to write it as y= something
you can do this by adding x^2 to both sides
so you end up with y = x^2 + 14
this is a function, it passes the vertical line test and is a parabola (you can graph it if you want to see what it looks like)

Answer 3

ok, so y is a function of x if it can be written in y= something form, and if it passes the vertical line test
It passes the vertical line test and is a function if there is nowhere on the graph where you can draw a line and have it go through two points on the graph (a circle, for example, would NOT pass the vertical line test, and is not a function of x)

so now, you have y-x^2 = 14
so you want to try to write it as y= something
you can do this by adding x^2 to both sides
so you end up with y = x^2 + 14
this is a function, it passes the vertical line test and is a parabola (you can graph it if you want to see what it looks like)

Answer 4

Y is always a function of X if you have an equation with both y and x present. If you wish to simplify this equation such that y = some function of X then this is what you do:

y-2x^2=14
+2x^2 +2x^2

y = 2x^2 + 14

Now, y is written in terms of x.