1. Formalizing Relations and Functions Section 4-6 Part 2 December 10, 2014

2. Goals Goal To determine whether a relation is a function. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

3. Give the domain and range of the relation. Tell whether the relation is a function. Explain. Draw in lines to see the domain and range values Range Domain Example:

4. Your Turn: Give the domain and range of each relation. Tell whether the relation is a function and explain.

5. Function Notation An algebraic expression that defines a function is a function rule. If x is the independent variable and y is the dependent variable, then function notation for y is f(x), read “ f of x, ” where f names the function. When an equation in two variables describes a function, you can use function notation to write it.

6. The dependent variable is a function of the independent variable. y is a function of x. y = f (x) Function Notation

7. Input x The x values, can be thought of as the inputs and the y values or f (x), can be thought of as the outputs. Output f (x) Function f Inputs & Outputs Independent variable Dependent variable

8. Evaluate the function for the given input values. For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4. Example: Evaluating Functions

9. Evaluate the function for the given input values. For, find h(r) when r = 600 and when r = –12. Example: Evaluating Functions

10. Evaluate the function for the given input values. For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3. Your Turn:

11. Evaluate each function for the given input values. For g(t) =, find g(t) when t = –24 and when t = 400. Your Turn:

12. Evaluate a Function The function w(x) = 250x represents the number of words w(x) you can read in x minutes. How many words can you read in 8 minutes?

13. Your Turn A car can travel 32 miles for each gallon of gasoline. The function d(x) = 32x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. The car’s fuel tank holds 17 gallons. How far can the car travel?

14. Identify a Reasonable Domain and Range You have 3 quarts of paint remaining after you finished painting your 1800 square foot home. A quart of paint covers 100 ft 2. The function A(q) = 100q + 1800 feet represents the area A(q), square feet, that q quarts of paint cover. What domain and range are reasonable for the function?