Linear Function

[nycmath]

For lines that are nonvertical, we use y = mx + b. This is called the slope-intercept form of the equation of a line. When the slope-intercept form of a line is written using function notation, the result is a linear function.

So, a linear function is a function of the form f(x) = mx + b.
The graph of a linear function is a line with slope m amd y-intercept b. Its domain and range is the set of all real numbers. Functions that are not linear are said to be nonlinear.

Questions

1. Is y = mx + b the same as f(x) = mx + b?

2. Why is the domain and range of a linear function the set of all real numbers?