Y = 1/X2 ==============Can it pass the line test? * * * * * That is not the inverse, but the reciprocal. Not the same thing! The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
x2+2x+1=y or y=x2 In this function the domain is x equals real values and the range is y equals all real values provided y is more than or equal to zero.
Y = X2 Is a parabolic function.
no, but y = x2 is a function
Y=X^2 is a function for it forms a parabola on a graph.
Y = 1/X2 ==============Can it pass the line test? * * * * * That is not the inverse, but the reciprocal. Not the same thing! The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
x2+2x+1=y or y=x2 In this function the domain is x equals real values and the range is y equals all real values provided y is more than or equal to zero.
y = -x2 + 1 This function describes a parabola that opens downward. To find the top of it's range, you need to find it's focal point. You can do that very easily by taking the derivative of the equation and solving it for 0: y = -x2 + 1 ∴ y' = -2x let y' = 0: 0 = -2x ∴ x = 0 Now you can calculate the y value at that point: y = -02 + 1 ∴ y = 1 So that function describes an upside down parabola whose peak is at the point {0, 1}. It's range then is: {y | y ∈ ℜ, y ≤ 1}
The answer, for y as a function of x, depends on the range of y. Over the real numbers, it is not a function because a function cannot be one-to-many. But it is always possible to define the domain and range in such a way that the mapping in not one-to-many.
Yes. Think of y as being a function of x. y = f(x) = x2 + 1
Y = X2 Is a parabolic function.
no, but y = x2 is a function
No. x2+5x is a polynomial, an algebraic expression or a formula, but it is not a function. It could be used to help define a function. {(x,y) | y = x2 + 5x , x any real number} is a function
Y=X^2 is a function for it forms a parabola on a graph.
The range depends on the domain. If the domain is the complex field, the range is also the whole of the complex field. If the domain is x = 0 then the range is 4.
y = x2 is the parent function, but it can be in the form y = ax2 + bx + c
x2 - y2 = (x + y)(x - y) is an identity, not a function.