5.4 Function Notation

Instead of y = mx +b, we can write linear functions like this:

f(x) = mx + b f(x) is read “f of x.” This means: The value of function f at x

It does NOT mean “f times x”

Function Notation

Can also use other letters (not just f!)

Examples: f(x) = 2x + 1 g(x) = -x – 6 h(x) = 4x – 2

When we need to evaluate a function for a given x value, it might say:“Find f(3)” - or - “Evaluate f(x) when x = 3”

This means: Find the output when the input is 3.

Evaluating f(x)

Example: Evaluate f(x) = -4x + 7 when x = 2.

Example: Let g(x) = -x – 1. Find g(4).

You Try! Let f(x) = 2x – 5. Evaluate the function when x = -4, 0, and 3.

f(-4) =

f(0) =

f(3) =

Solving for the Independent Variable For find the value of x for which h(x) = -7.

Example For find the value of x so that f(x) = 21.

You Try! For find the value of x so that g(x) = -1.

Graphing To graph in function notation:

Remember: f(x), g(x), h(x) just replace the y in y = mx + b

(0, b) is still the y-intm is still the slope

Example Graph f(x) = 2x + 5

You Try! Graph:

Investigation Graph each function on the same graph.

f(x) = 2x g(x) = 2x + 3 h(x) = 2x – 3

What do you notice about these 3 graphs?

Vertical Translations The graph of f(x) + k is a vertical translation (shift) of the graph of f(x).

Lines have the same slope but different y-intercepts.

Example: Compare the graph of g(x) = x – 3 to the graph of f(x) = x.

You Try! Compare each graph to the graph of f(x) = -3x:

g(x) = -3x + 4

h(x) = -3x – 5