|
Linear Functions: Any function of the form
f (x) = m x + b, where m is not equal to 0 is called a linear function. The
domain of this function is the set of all real numbers. The range of f is the
set of all real numbers. The graph of f is a line with slope m and y intercept
b.
Note: A function f (x) = b, where b is a constant real
number is called a constant function. Its graph is a horizontal line at y = b.
Example 1: Graph the linear function f given by
f (x) = 2x + 4
Solution to Example 1
-
You need only two points to graph a linear
function. These points may be chosen as the x and y intercepts of the graph for
example.
-
Determine the x intercept, set f(x) = 0 and
solve for x.
-
Determine the y intercept, set x = 0 to find
f(0).
-
The graph of the above function is a line passing through
the points (-2 , 0) and (0 , 4) as shown below.
Matched Problem : Graph the linear function f given by
f (x) = x + 3
Example 2: Graph the linear function f given by
f (x) = -(1 / 3)x - 1 / 2
Solution to Example 2
- Determine the x intercept, set f(x) = 0 and
solve for x.
-(1 / 3)x - 1 / 2 = 0
x = - 3 / 2
- Determine the y intercept, set x = 0 to find
f(0).
-
The graph of the above function is a line passing through
the points (-3 / 2 , 0) and (0 , -1 / 2) as shown below.
Matched Problem : Graph the linear function f given by
f (x) = -x / 5 + 1 / 3
More references and links to graphing and graphs of functions.
Graphing Functions
|