IM Alg1.4.4 Lesson: Using Function Notation to Describe Rules (Part 1)
What do you notice? What do you wonder?
Here are descriptions and equations that represent four functions.
Match each equation with a verbal description that represents the same function. Record your results.
For one of the functions above, when the input is 6, the output is -3. Which is that function: , , , or ? Explain how you know.
Which function value— , or —is the greatest when the input is 0?
Which function value— , or —is the greatest when the input is 10?
Mai says is always greater than for the same value of . Is this true? Explain how you know.
A square that has a side length of 9 cm has an area of 81 cm² . The relationship between the side length and the area of the square is a function. Complete the table with the area for each given side length.
Then, write a rule for a function, , that gives the area of the square in cm² when the side length is cm. Use function notation.
What does represent in this situation? What is its value?
On the coordinate plane, sketch a graph of this function.
A roll of paper that is 3 feet wide can be cut to any length.
If we cut a length of 2.5 feet, what is the perimeter of the paper? 
Complete the table with the perimeter for each given side length.
Then, write a rule for a function, , that gives the perimeter of the paper in feet when the side length in feet is . Use function notation.
What does represent in this situation? What is its value?