We know that equations of various figures can be graphed including those of conic sections (circles, ellipses, hyperbolas and parabolas), lines etc. However, we cannot consider all of these equations as Functions. In practice we define functions as those equations in mathematics which have unique output for each input. The equation of circles cannot be considered as function as here one input can give you two outputs. So, let us understand how to write an equation in function form.
The vertical line test can be used to determine whether your equation is a function or not. This means for only one value of 'y' we should get our equation satisfied. That is a unique output for each input. Let’s consider an example to check for the function form: Say we have an equation given as 'y' - 200 = 150x, adding 200 to both sides we get, y = 150x + 200.
First determine on what variable your function depends upon. Like in our case variable is 'x'. The function value changes as 'x' changes, so function is dependent upon 'x'.
It is not required for functions to be linear. For instance, function h(v) = -v2 – 3v + 5 is not linear. The equation is nonlinear because of power of 'v' i.e. square, but it is still a function because there is a unique value of h(v) for every value of 'v'. When you are evaluating the value of a function, place the value of variable in parenthesis rather than variable. For example: we have f(x) = 21x + 4, to find the value of the function f(x) at x = 4 write the value 4 in parenthesis as f (4) = 21 *4 + 4 = 88. Similarly, f(0) = 4 and f(1) = 25.