The function represented by an equation with xxx as the independent variable can be written using function notation by expressing the dependent variable (usually yyy) as a function of xxx, denoted as f(x)f(x)f(x). For example, given the equation 9x+3y=129x+3y=129x+3y=12 with xxx as the independent variable:
- Solve the equation for yyy:
3y=12−9x3y=12-9x3y=12−9x
y=12−9x3=4−3xy=\frac{12-9x}{3}=4-3xy=312−9x=4−3x
- Replace yyy with the function notation f(x)f(x)f(x):
f(x)=4−3xf(x)=4-3xf(x)=4−3x
This expresses the function using notation where f(x)f(x)f(x) indicates the function of the independent variable xxx. This form simplifies understanding and working with the function.
