1. LESSON 7.4 Function Notation To learn function notation To evaluate functions by substitution, by using the graphs drawn by hand, and on the graphing calculator.

2. Every function defines a relationship between an input (independent) variable and an output (dependent) variable. Function notation uses parentheses to name the input.

3. You can show some functions with equations. ◦ y=2x+4 also represents a function so we can write f(x)=2x+4. ◦ f(3) means we want to substitute 3 for x in the equation y=2x+4. So f(3)=2(3)+4 or 10. ◦ f is the name of the function.

4. Not all functions are expressed as equations. The graph below shows a new function, f(x). No equation or rule is given. There are still input and output values. f(4)=1 Can you find two values for which f(x)=1?

5. Describe the domain and range of the function f in the graph. input output Use the graph to find each function value in the table. Then do the indicated operations. 5 21 12 5 18

6. Use the rules for the order of operations to evaluate these expressions that involve function values. Do any operations inside parentheses first. Then use the graph to find the function values before doing the remaining operations. Write your answers in a table. input output 12 5 15 14 8 1 18 4

7. 5 21 12 5 18 Think of the numbers 1 through 26 as the letters A through Z. Find the letters that match your answers to Step 2 to learn the mathematician's last name. Find the letters that match your answers to Step 3 to discover the first name. 12 5 15 14 8 1 18 4 Step 3 Step 4