# Lesson 8

Representing Functions

- Let’s represent functions.

### 8.1: The Secret Club

In a secret club, everyone is known by the month they were born. So Diego would be called “January” and Tyler would be called “August.”

- What would be the name of some people in your class in the secret club?
- Why might club meetings get kind of confusing?
- Can you think of a better system for assigning club members new names?

### 8.2: Examples of Functions

- For each question, answer yes or no.
- It is 50 miles to Tucson. Can we figure out how many kilometers it is to Tucson?
- It is 200 kilometers to Saskatoon. Can we figure out how many miles it is to Saskatoon?
- A number is -3. Can we figure out its absolute value?
- The absolute value of a number is 8. Can we figure out the number?
- A circle has a diameter of 8 cm. Can we figure out its circumference?
- A circle has a circumference of \(10\pi\) cm. Can we figure out its diameter?
- A square has a side length of 6 units. Can we figure out its perimeter?
- A rectangle has a perimeter of 30 meters. Can we figure out its width?

- Which of the relationships are functions?
- For each function definition in the table, match it with the situation, write a statement explaining which variable depends on which, and write an example using function notation. An example is done for you.
function definition situation statement example \(m(x) = 0.62x \) You know kilometers and want to find miles. Distance in miles depends on distance in kilometers, or, distance in miles is a function of distance in kilometers. \(m(100)=62\) \(f(x) = x \boldcdot \pi\)

\(g(x) = 1.6x\)

\(h(x) = 4x\)

\(k(x) = |x|\)

### 8.3: Matching Representations

Your teacher will give you a set of representations. Sort them so that in each group there is a table, graph, equation, and example that all represent the same function.