math

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How do I know that x^2-7=y is a function? thanks

you know its a function because its a parabola (x^2)

parabolas are functions because there is only one x value per y value.

So I know it is a function because it has (x^2)? Is that the rule? If it has x^2, it's a function and if it doesn't, it's not a function?

no, its a function if there is only one x value per y value. for example, a circle is not a function, because there are two y values for one x value.

if something is an x^2, you know its a parabola. and a parabola is one of many examples of a function.

How do you tell if there is only one x per y by just looking at an equation such as (x-4)/3=y?

generally, if the equation can be solved for y as a single expression in such a way that the other side contains only x's and constants, then it is a function.

if, when graphed, you visualize a vertical line scanning from left to right, if the vertical line crosses or touches the graph in more than one place for any value of x then it is NOT a function (the verical line test)

what is a constant?

so are most equations usually functions unless y=a squareroot, such as y=sqrtx+6

a constant is a numerical value without a variabe
eg. in y = 7x+5, the 5 is a constant.

even equations like y=SQR(x^2-9) are considered functions, since by the definition the SQR yields only a positive result.

However when you have somthing like
x^2+y^2=100, which is a circle, then when you solve for y you would get
y^=100-x^2 and then
+y=SQR(100-x^2) or -y=SQR(100-x^2)
which we normally write as
y=+/-SQR(100-x^2)
notice that y is written as two different equations, thus NO function

yeah, that's what i meant, when the answer is a squareroot

y=sqrt(100-x^2) would be a function since y was written as a single unique expression and for each x of the domain you got one and only one y value.

but isn't the answer y=+sqrt(100-x^2)
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