Lesson 4.7: Function Notation

CHAPTER 4 Test on _________________

Lesson 4.7: Function Notation

You have seen linear functions written in the form y = mx + b. You can name a function f(x) by writing it in function notation.

Symbol "f of x" (means the same thing as "y")

Function notation: f(x) = mx + b

The symbol f(x) is another name for y and is read as "the value of f at x", or simply as "f of x." It does NOT mean f times x. You can use letters other than f, such as g or h, to name functions.

Examples of Function Notation:

f(x) = 7x - 4 g(t) = 3t + 9 h(r) = -2r - 3

So what is a function again?

A function is a rule that takes an INPUT and turns it into an OUTPUT. (Think factory/conveyor belt)

Function: f(x) = 7x - 4 Input: x = 3 Output: = ?

To evaluate a function, simply plug-in the input into the function and find the output value!

EXAMPLE 1:

EXAMPLE 2:

Evaluate the function h(x) = ?7x - 11 when x = 7.

EXAMPLE 3: Finding an x value (input).

For the function f(x) = 2x - 10, find the value of x so that the function value f(x) = 6.

EXAMPLE 4:

f(x) = 5x +3 Find x so that f(x) = -12.

Example 3: Graph a function.

The gray wolf population in central Idaho was monitored over several years for a project aimed at boosting the number of wolves. The number of wolves can be modeled by the function f(x) = 37x + 7, where x is the number of years since 1995. Make a table and graph the function.

Number of Wolves

180 150 120 90 60 30

01 2 34

Years Since 1995

X (input)

Y (output)

CURRENT WOLF POPULATION : Use the model from Example 3 to estimate how many wolves will be present in Idaho in 2012.

A family of functions is a group of functions with similar characteristics. For example, functions that have the format f(x) = mx + b constitute the family of linear functions.

f(x) = 2x +3 g(x) = (1/4)x -7

h(x) = 33x j(x) = -8

The most basic linear function in the family of all linear functions is called the parent function. The parent linear function is: f(x) = x.

The function f(x) = x has a y-intercept of 0 and a slope of 1.

f(x) = x

Example 4: Graph the functions and compare graphs with the graph of f(x) = x.

a. g(x) = x + 3

f(x) = x

You must compare 3 things: a) steepness of slopes b) y-intercepts c) direction of the line

b. h(x) = 2x

c. h(x) = (-1/3)x

4.7 Function Notation - Summary

So what is a function again?

A function is a rule that takes an INPUT and turns it into an OUTPUT. (Think factory/conveyor belt)

Function: f(x) = 7x - 4 Input: x = 3 Output: f(x) = ?

The formal way to name or represent a function is replacing the "y" with the symbol "f(x)". This is called function notation.

Function notation: f(x) = mx + b

f(x) IS JUST A SYMBOL. It is another name for y and is read as "f of x." It does NOT mean f times x.

Example: Given the function f(x) = -3x - 4 a) Evaluate the function f(x) when x = 10. b) Evaluate the function f(x) when x = -4

Example: Given the function g(t) = -5t + 1 a) Find the value of t so that the function has a value of g(t) = -14. b) Find the value of t so that the function has a value of g(t) = 31.

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