2. Identifying from an equation: Linear y = mx +b Has an x with no exponent (or exponent 1). Examples: y = 5x + 1 y = ½x 2x + 3y = 6 Quadratic y = ax 2 + bx + c Has an x 2 in the equation. Examples: y = 2x 2 + 3x – 5 y = x 2 + 9 x 2 + 4y = 7 Exponential y = ab x Has an x as the exponent. Examples: y = 3 x + 1 y = 5 2x 4 x + y = 13

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

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

5. LINEAR, QUADRATIC, EXPONENTIAL, OR NEITHER? a)b) c)d)

6. Is the table linear, quadratic or exponential? Quadratic See same y more than once. Linear Never see the same y value twice. Can be written as: Next = Now + m, SA: b Exponential y changes more quickly than x. Never see the same y value twice. Can be written as: Next = Now  b, SA: a

7. Identifying functions given a table of values EXAMPLE 1 x – 2– 10 1 2 y – 2 1 4 7 10 3 3 3 3 b. Next = Now + 3, SA: 4  y = 3x +4  Linear Function

8. Identifying functions given a table of values EXAMPLE 2 Does the table of values represent a linear function, an exponential function, or a quadratic function? x–2–1012 y0.250.5124 2 2 2 2 a. Next = Now  2, SA: 1  y = 1(2) x  Exponential Function

9. Identifying functions given a table of values EXAMPLE 3 Determine which type of function the table of values represents. x –2 –10 1 2 y 2 0.5 0 2 –1.5 –0.5 0.5 1.5 Notice that there are two y-values associated with an x-value: (-2,2) and (2,2)  Quadratic Function

10. 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

11. Identifying Regressions Using Shapes of Known Functions

12. Fitting Functions to Data The term regression pertains to the process of finding an equation for the relationship seen in a scatter plot. Regression is a generic term for all methods attempting to fit a model to observed data in order to predict new values. Steps for finding a regression: 1. Create a scatter plot:

13. Creating a Scatter Plot 9 Zoom Stat

14. Go to STAT, arrow right to CALC, and arrow down for regression equation choices.