Comparing Linear, Exponential, and Quadratic Functions.

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Presentation transcript:

Comparing Linear, Exponential, and Quadratic Functions

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 = ax2 + bx + c Has an x2 in the equation. Examples: y = 2x2 + 3x – 5 y = x2 + 9 x2 + 4y = 7 Exponential y = abx Has an x as the exponent. Examples: y = 3x + 1 y = 52x 4x + y = 13

Examples: LINEAR, QUADRATIC or EXPONENTIAL? y = 6x + 3 y = 7x2 +5x – 2

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

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

Identifying functions given a table of values EXAMPLE 2 Identifying functions given a table of values Does the table of values represent a linear function, an exponential function, or a quadratic function? a. x –2 –1 1 2 y 0.25 0.5 4 2 2 2 2 Next = Now  2, SA: 1  y = 1(2)x  Exponential Function

Identifying functions given a table of values EXAMPLE 3 Identifying functions given a table of values Determine which type of function the table of values represents. x –2 –1 1 2 y 0.5 –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

Is the table linear, quadratic or exponential? y 1 2 -1 3 4 5 8 x y 1 3 2 9 27 4 81 5 243 x y 1 5 2 9 3 13 4 17 21

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.