For y=5x^2.... is x a function of y?

Question

OH SHOOT! lol
I MEANT IS Y A FUNCTION OF X!!!!!

Answer 1

y is a function of x because no x-value yields more than one y-value.

Answer 2

It has been a long time since I looked at something like this,

y=5x^2 is a parabula - so for every value of x there is only 1 y value i.e. x=2, Y = 20
however if you rearrange the question for every value of y there are 2 possible x values
for example y=20 x = 2 or x =-2

If I remember right - draw the graph (e.g. plug in x=-2, -1, 0, 1 and 2 ---> plot this on a graph
If you turn the graph sideways and draw a vertical line through the funtion you get 2 answers for every y value except 0.

I can't remember if this disqualifies it as a funtion or is just an interesting fact x=+/- Sqroot(y/5)

Answer 3

Yes y is function of x. You can also write this as x=√[y/5] or x=-√[y/5], and you have expressed the same relation but as x a function of y. Which is a function of which depends on what you consider the independent variable (one that you have or can set values for); in general when equations are written in x, x is the independent variable, and the equation is considered a function of x.

Answer 4

Writing the value of x:
x = (y/5)^1/2
Let y1 and y2 correspond to same value of x
Then ( y1 /5 )^1/2 = ( y2 /5)^1/2
or by simplification, y1 = y2.
Thus we can say y is a function of x.
You can also verify this by plotting a graph . If you you draw a vertical at any value of x it never intersects at more than once the curve.

Answer 5

Yes it is, because the answer of y DEPENDS on the x-value that is inputted into the equation.

Answer 6

yes

Answer 7

yes