Identifying from an equation: Linear y = mx +b Has an x with no exponent (or exponent 1). Examples: y = 5x + 1 y = x 2x + 3y = 6 Quadratic y = ax 2 + bx + c Has an x 2 in the equation. Examples: y = 2x 2 + 3x 5 y = x 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 Examples: LINEAR, QUADRATIC or EXPONENTIAL? a) y = 6 x + 3 b) y = 7x 2 +5x 2 c) 9x + 3 = y d) 4 2x = 8 Identifying from a graph: Linear Makes a straight line Quadratic Makes a U or Exponential Rises or falls quickly in one direction LINEAR, QUADRATIC, EXPONENTIAL, OR NEITHER? a)b) c)d) 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 Identifying functions given a table of values EXAMPLE 1 x 2 y b. Next = Now + 3, SA: 4 y = 3x +4 Linear Function 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? x21012 y a. Next = Now 2, SA: 1 y = 1(2) x Exponential Function Identifying functions given a table of values EXAMPLE 3 Determine which type of function the table of values represents. x 2 y 1.5 Notice that there are two y-values associated with an x-value: (-2,2) and (2,2) Quadratic Function Is the table linear, quadratic or exponential? xy xy xy Identifying Regressions Using Shapes of Known Functions 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: Creating a Scatter Plot 9 Zoom Stat Go to STAT, arrow right to CALC, and arrow down for regression equation choices.