You need it in the form f(x)= ... (whatever your equation happens to be).
i.e get the equation in the form y=... Then swap the 'y' for 'f(x)'. Simple.
It means you should rearrange the equation so that x is on one side of the equal sign, and everything else on the other, with no "x" on the right side of the equation. For instance, if I was told to express x as a function of y and given the equation: x-4y=6 I would express x as a function of y by rearranging the equation to read: x = 6+4y
The set of all values of x, for which the equation is true is the domain of the function defined by that equation.
You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.
An equation where the left is the function of the right. f(x)=x+3 is function notation. The answer is a function of what x is. f(g(x))= the answer the inside function substituted in the outside function.
The equation for a circle is a function in that it can be graphed and charted. One common equation is x^2 + y^2 = r^2.
f (x) = 2/3 x + 2
It would be rewritten as y=(2/5)x+3
1) Solve the equation for the desired variable. 2) Write it in function notation. For example, if y = 2x + 3, it is already solved for "y"; just rewrite it as f(x) = 2x + 3.
To rewrite the equation (-3x + 4y - 5 - 14 = 0) so that (y) is a function of (x), first simplify the equation to (-3x + 4y - 19 = 0). Then isolate (y) by adding (3x + 19) to both sides: (4y = 3x + 19). Finally, divide by 4 to solve for (y): (y = \frac{3x + 19}{4}).
Any equation which maps each value of x in the domain to a value in the range is a function of x.
To find the inverse of a function, you swap the input and output variables. For a function expressed as ( y = f(x) ), you rewrite it as ( x = f(y) ) and then solve for ( y ) in terms of ( x ). The resulting equation represents the inverse function, typically denoted as ( f^{-1}(x) ). Finally, it's essential to verify that the composition of the function and its inverse returns the original input.
y=3x+12
You can rewrite the equation as... 100=10x X=2
y=-x+8
y = -x-2
An example of a wrong function equation is f(x) = sqrt(x) for all non-negative x.
No. A function need not be linear. For example, y = sin(x) is a function of x but it is not a linear equation.