Is this a function?

Question

14 + 10x squared = 7y squared ...Please explain why or why not this is a function..and how you came up with the answer..thanks.

Answer 1

Hey,

No, this is not a function. Let me explain why: if we were to solve for y alone, we would first divide by 7 and then take the square root of y. Once we take the square root of y, we now need to make sure that the other side of the equation says: +/- the square root.

Notice that this leads us with one vale of x gives us 2 values of y. A function would only have one x value give us 1 y-value.

Therefore, this isn't a function!

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 2

14 + 10x^2 = 7y ^2
y^2 = 2 + 10x^2/7
y = +/- sqrt(2+10x^2/7)
You should note that for any unique value of x there will be two values of y (one negative and one positive). Thus it is not a function. To be a function, there must be only one value of y for each value of x.

Answer 3

This is an equation where for given values of x and y the equation will hold true. A function is of the form y=f(x), where the value y is solely dependant on the single variable x when input into the function f, i.e. for every value of x there is one and only one corresponding value of y and the relationship can be plotted on a graph. Additionally, an expression of the form y=f(x,w,z..) is called a formula where the value of y is dependant on a number of independant variables.

Answer 4

This is not a function because for each x value, you have two y values.
y = ±√[(14+10x^2)/7]

Answer 5

No. It is an equation. A fuction may be expressed in f(x) or f as a quantity of x