Posted by Mimi on Tuesday, March 20, 2007 at 4:57pm.
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)
-
No one has answered this question yet.
Answer this Question
Related Questions
pre calc - The Identity Function The Squaring Function The Cubing Function The ...
math - (a) In order to express the function y = 1010 x + 4, as a composition of ...
math - Question-2; Consider the function f(x)= -cos3x -4sin3x. (a)Find the ...
Math - What are the similarities and differences between functions and linear ...
Math - What are the similarities and differences between functions and linear ...
Calculus - In order to express the function y=12^19x+7 as a composition of two ...
Math: Parabola, Vertex - Find the vertex of the parabola associated with the ...
Gr.11 - Rational functions graphing. - 1. Identify a rational function whose ...
maths(urgent)thanks. - a parabola with turning point at (1,-2) and passing ...
Algebra - Can you please help me with the following problems? Find the ...
For Further Reading
