Determine whether y^2=2x^2−1 is a function.

Question

I am thinking that this is true but worried that I am wrong

Answer 1

graphically, the equation describes a hyperbola

y^2 =2x^2 -1

2x^2 -y^2 = 1

x^2/(sqr2/2)^ -y^2 = 1

It fails the vertical line test. vertical lines intersect the hyperbola twice. That means it's not a function

let x=1, then y = -1 or +1, if there is not a unique value of y for any value of x, then it's not a function.

to be a function there has to be one and only one output for every input. x is the input, y is the output for an input of 1, there are 2 possible outputs, 1 or -1

or use a graphing calculator and try drawing a vertical line through the graph. IF it cuts twice, it's not a function.