8.6 Linear, Exponential, and Quadratic Functions

What We Will Learn Choose appropriate function Story problems

Ex. 1 Using Graphs to Identify Functions Core Concept:

Ex. 1 continued Plot the points and tell what kind of function it is. (4,4), (2,0), (0,0), (1,-.5), (-2,4) quadratic

Ex. 2 Identifying From a Table Looking at y’s Linear: first differences are constant by adding or subtracting Exponential: y values are multiplying or dividing Quadratic: second differences are constant by adding or subtracting Linear X -3 -2 -1 1 Y 11 8 5 2 -3 -3 -3 -3 First differences

Ex. 2 Continued exponential quadratic X -2 -1 1 2 Y 4 8 16 X -2 -1 1 2 1 2 Y 4 8 16 X -2 -1 1 2 Y 7 x2 x2 x2 x2 -1 +1 +3 +5 First differences +2 +2 +2 Second differences

Ex. 5 Story Problems In 1900, Littleton had a population of 1000 people. Littleton’s population increased by 50 people each year. In 1900, Tinyville had a population of 500 people. Tinyville’s population increased by 5% each year. A. In what year were the populations about equal? B. Suppose Littleton’s initial population was 2000 and maintained the constant rate of change. Did Tinyville still catch up to Littleton and in what year? C. Did Tinyville still catch up to Littleton is start with 2000 people and changes by 100 people per year? D. Why did Tinyville always catch up to Littleton?