1. Function Notation & Evaluating Functions
Algebra with Wiggins

2. What is function notation?
Function notation is a method for writing variables as a function of other variables.
The variable y, becomes a function of x, meaning the variable x is used to find the value of y.
Example: If Jerrell plans to take members of his basketball team out to eat for each, how much money will Jerrell need?
Y = 9.99x

3. When can function notation be used?
When the set of ordered pairs described by an equation satisfies the definition of a function, the equation can be written in function notation.

4. Does not mean multiplication!
Function notation replaces the independent variable, y with either f(x), g(x), or h(x).
Does not mean multiplication!
f(x) is read as “ _f___ ___of__ ____x_”
g(x) is read as “ _g___ ___of__ __x___”
h(x) is read as “ __h__ __of___ __x___”

5. Instead of writing, y = x + 3, we replace the y with f (x) f(x) = x + 3
Is read as “ f of x equals x+ 3

7. Independent and Dependent Variables Expressed in Function Notation
Write each of the following sentences in function notation by choosing meaningful letters to represent each variable.
Then identify the independent variable (input) and the dependent variable (output).
a. A person’s weight is a function of the person’s height.
b. The current gas price is a function of the amount of available crude oil.

8. Example Solution
a. Selecting w for the person’s weight and h for the height, we represent this function as f (h) = w. The function f takes a value for the independent variable h and generates a value for the dependent variable w.
b. Selecting g for the gas price and c for the available crude oil, we represent this function as f (c) = g. The function f will take a value for the independent variable c and generates a value for the dependent variable g.

9. Evaluating Functions
We can evaluate functions using function notation.
The process of finding the output of a function that corresponds with a given input is called evaluating a function.

10. Suppose that your current job pays $11. 50 per hour
Suppose that your current job pays $11.50 per hour. Your salary, S, is calculated by multiplying $11.50 by the number of hours you work, h. That is, Salary = $11.50? Hours or, in function notation, S = f (h) = 11.5h. Evaluate f (80) and explain what the numerical answer means.
Solution:
To evaluate f (80) means to find the numerical value of S that results from “plugging in” 80 for the number of hours.

11. We have
f(h) = 11.5h
f(80) = 11.5(80)
= 920
In other words, when h = 80, S = 920. This means that if you work 80 hours your salary will be $920.

12. Find the range for the function f(x) = 3x + 1
If the domain of f(x) is {0, 2,4}.

13. Practice Problems Evaluate the Functions
Evaluate h(x) =
2𝑥 2 − 3x - 2
h(0)
h(2)
h(3)