# Let's Get Started

**TEKS Standards and Student Expectations**

**A(12) **Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to:

**A(12)(B) **evaluate functions, expressed in function notation, given one or more elements in their domains

**Resource Objective(s)**

Given verbal and symbolic representations of a function, the student will find specific function values.

**Essential Questions**

What method can be used to find the value of a function?

How is function notation similar to *y*-notation?

How is function notation different from *y*-notation?

**Vocabulary**

# The Function Machine

We're going to use an interactive function machine and record the *x*-value, *y*-value, and function on your own paper.

**Directions**

Make at least three tables on your own paper similar to the table shown below.

x |
y |

- Using the interactive, input a value for
*x*. When you input a value for*x*, a value for*y*will be given (output). - Record the value for
*y*in your table. Use the drop down menu to choose the operational sign, and then enter your guess. - Click the "Check formula" button to check your answer.
- Click the "Set new function" button and repeat the steps two more times. Be sure to create two more tables on your own paper.

# The Connection Between y = and Function Notation

Having familiarized ourselves with a function machine, it is time to look at the relationship between y= and function notation, including how these notations can be used to develop a table of values.

Follow the link below to view a video that explains this relationship.

# Function Values

Functions are often represented using function notation. As you can see in the following video, function notation is usually written with a lower or uppercase letters—such as f, g, or H—followed by a variable in a parenthesis. The function "f(*x*)" is read as “f of *x*” and does not imply multiplication between the two variables. It’s just a mathematical way of giving the rule that can be used to generate a table of values.

Watch the following video to discover how to find specific values for functions. After viewing the video, use your notes to explain how function notation is similar to *y* = notation and how to find specific function values.