1. Example 1 Identify Functions Identify the domain and range. Then tell whether the relation is a function. Explain. a. b. SOLUTION a. The domain consists of the inputs: 2, 1, and 4. The range consists of the outputs: 3, 1, 2, and 3. The relation is not a function because the input 1 is mapped onto both 3 and 1. – – –

2. Example 1 Identify Functions The domain consists of the inputs: 3, 2, 1, and 4. The range consists of the outputs: 3, 1, and 1. The relation is a function because each input is mapped onto exactly one output. b. – –– –

3. Checkpoint Identify the domain and range. Then tell whether the relation is a function. Explain. 1. ANSWER The domain consists of inputs: 1, 2, 3, 4, the range consists of outputs: 2, 1 ; the relation is a function; each input is mapped onto exactly one output. – – Identify Functions

4. Checkpoint ANSWER The domain consists of inputs: 0, 2, 3, the range consists of outputs: 1, 2, 3 ; the relation is not a function; the inputs 0 and 2 are each mapped onto two different outputs. Identify the domain and range. Then tell whether the relation is a function. Explain. 2. Identify Functions

5. Checkpoint Identify the domain and range. Then tell whether the relation is a function. Explain. 3. ANSWER The domain consists of inputs: 2, 0, 2, 4, the range consists of the output: 4 ; the relation is a function; each input is mapped onto exactly one output. – – Identify Functions

6. Example 2 Apply the Vertical Line Test Graph the relations above. Use the vertical line test to tell whether the relations are functions. a. First, write the relation as a set of ordered pairs. ( ),), 1, 1 ( ),), 2, 2 – ( ),), 1, 3 – () 4, 3 a. b.

7. Example 2 Apply the Vertical Line Test Then plot the points. The vertical line at x 1 contains two different points in the relation. So, the relation is not a function. = b. First, write the relation as a set of ordered pairs. ( ),), 1, 1 ( ),), 3, 1 –– ( ),), 2, 1 – () 4, 3 – No vertical line contains more than one point in the relation. So, the relation is a function. Then plot the points.

8. Checkpoint Graph the relation shown in the diagram.4. ANSWER Apply the Vertical Line Test

9. Checkpoint Explain how to use the vertical line test to show whether the relation is a function. 5. ANSWER The vertical line at contains two different points in the relation. So, the relation is not a function. 2x = – Apply the Vertical Line Test

10. Example 3 Graph an Equation Graph. y 1x=+ Plot the points. Notice that all the points lie on a line. STEP 2 SOLUTION STEP 1 Make a table of values, and write the ordered pairs. Evaluate y 0 0 1 1 2 2 3 Choose x 2 – 1 – 1 – () x, yx, y () 2, 1 –– () 1, 0 – () 0, 1 () 1, 2 () 2, 3 :,,,,

11. Example 3 Graph an Equation STEP 3 Connect the points with a line. Observe that the graph represents a function.

12. Example 4 Graph a Real-World Equation Hang Gliding A hang glider at a height of 450 feet begins descending at a rate of 10 feet per second. The height h in feet after descending for t seconds is given by: h10t450= – Graph the equation. Use input values of t 0, 10, 20, and 30 seconds. =

13. Example 4 Graph a Real-World Equation Plot the ordered pairs.STEP 2 Connect the points with a line. STEP 3 STEP 1 Make a table of values, and write the ordered pairs. SOLUTION h 350 t 010 450 250 20 150 30 () t, ht, h () 0, 450 () 10, 350 () 20, 250 () 30, 150 :,,,

14. Checkpoint ANSWER Graph the equation. 6.6. y3x = – Graph an Equation

15. Checkpoint ANSWER Graph the equation. 7.7. 4 x + – Graph an Equation y =

16. Checkpoint Graph the equation. ANSWER Graph an Equation 8.8. 3 2x2x + y =