Office Note

When a function is expressed as an equation, it is often written as "f(ten) ." In creating a table of values for an equation, for example y = 5x - 1, we use this rule, "multiply by 5 and subtract one" to transform an input x value into the one resulting y value. By giving the expression "multiply by five and subtract one" the name f, we accept an easy way to testify that nosotros're applying the rule to unlike numbers and variables.

In general, the symbol f(ten) replaces y and is read as f of x , which does non mean f times ten.  It ways the value of expression f for a given value of x.

Instance

Evaluate the function for the given value of the variable.

f(x) = 5x - 1 when x = three

Graphing a Linear Function

Since the office annotation lets us write f(ten) instead of y, the graph of a office f is the prepare of all points (ten, f(x)), where x is in the domain of the role.

Example

Graph f(x) = 5x - 1 and observe the value of f(three) past using the graph.

The y-intercept is -1 and the slope is 5. When x = 3, y equals xiv. This confirms the answer establish in the previous example.