1. Warm-up 1. Graph y = 3 x. ANSWER Tell whether the ordered pairs (0, 0), (1, 2), (2, 4), and (3, 6) represent a linear function. 2. For y = x 2 – 3x – 5, find corresponding y -values for the x -values –2, 1, and 3. 3.

2. 10.8 Compare Linear, Exponential, and Quadratic Models Students will Compare Linear, Exponential, and Quadratic Models

3. Identifying from an equation: Linear Has an x with no exponent. y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic Has an x 2 in the equation. y = 2x 2 + 3x – 5 y = x 2 + 9 x 2 + 4y = 7 Exponential Has an x as the exponent. y = 3 x + 1 y = 5 2x 4 x + y = 13

4. Examples: LINEAR, QUADRATIC or EXPONENTIAL? a)y = 6 x + 3 b)y = 7x 2 +5x – 2 c)9x + 3 = y d)4 2x = 8

5. Identifying from a graph: Linear Makes a straight line Quadratic Makes a U or ∩ Exponential Rises or falls quickly in one direction

6. LINEAR, QUADRATIC or EXPONENTIAL? a)b) c)d)

7. Is the table linear, quadratic or exponential? Quadratic See same y more than once. 2 nd difference is the same Linear Never see the same y value twice. 1 st difference is the same Exponential y changes more quickly than x. Never see the same y value twice. Common multiplication pattern

8. Identify functions using differences or ratios EXAMPLE 2 ANSWER The table of values represents a linear function. x – 2– 10 1 2 y – 2 1 4 7 10 Differences: 3 3 3 3 b.

9. Identify functions using differences or ratios EXAMPLE 2 Use differences or ratios to tell whether the table of values represents a linear function, an exponential function, or a quadratic function. ANSWER The table of values represents a quadratic function. x–2–1012 y–6 –406 First differences: 0 2 4 6 Second differences: 2 2 2 a.

10. GUIDED PRACTICE for Examples 1 and 2 2. Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. ANSWER exponential function 0 y 2 x – 2– 1 1 0.08 0.4 10

11. xy 0-5 1-4 2 34 411 xy -2 -4 0-8 2-32 5-256

12. Is the table linear, quadratic or exponential? xy 10 2 30 43 58 xy 15 29 313 417 521 xy 13 29 327 481 5243

13. Write an equation for a function EXAMPLE 3 Tell whether the table of values represents a linear function, an exponential function, or a quadratic function. Then write an equation for the function. x –2 –10 1 2 y 2 0.5 0 2

14. SOLUTION Write an equation for a function EXAMPLE 3 STEP 1 Determine which type of function the table of values represents. x –2 –10 1 2 y 2 0.5 0 2 First differences: –1.5 –0.5 0.5 1.5 Second differences: 1 1 1