Linear, Quadratic, and Exponential Models
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Name______Date______Class______Practice B Linear, Quadratic, and Exponential Models Graph each data set. Which kind of model best describes the data? 1. {(2, 0), (1, 3), (0, 4), (1, 3), (2, 0)} 2. {(0, 3), (1, 6), (2, 12), (3, 24), (4, 48)}
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Look for a pattern in each data set to determine which kind of model best describes the data. 3. {(5, 9), (4, 0), (3, 7), (2, 12)} ______4. {(2, 9), (1, 13), (0, 17), (1, 21)} ______5. {(1, 4), (2, 6), (3, 9), (4, 13.5)} ______6. {(0, 4), (2, 12), (4, 36), (6, 76)} ______ 1 1 1 7. (1,17), 3, 8 , 5, 4 , 7, 2 ______ 2 4 8 8. Use the data in the table to describe Restaurant how the restaurant’s sales are changing. Year 0 1 2 3 Then write a function that models the data. Use your function to predict the Sales 20,000 19,000 18,050 17,147.50 amount of sales after 8 years. ($) ______9. Use the data in the table to describe Clothing Store how the clothing store’s sales are changing. Then write a function that Year 0 1 2 3 models the data. Use your function Sales 15,000 15,750 16,500 17,250 to predict the amount of sales ($) after 10 years. ______
Practice B Comparing Functions 1. Three functions are given below. Complete the tables and find the rate of change over [0, 3] for each function. Then graph all three functions on the same coordinate plane.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Algebra 1 Name______Date______Class______
y 4x 10 y 1 4x y 4x2 4x x y x y x y 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4
Rate of change ______a. Compare the rates of change. ______b. How do the y-values at x 0 and x 3 relate to the rates of change over [0, 3]? ______2. An engineer designs headlight reflectors. Equations for the shapes of two of his designs are shown below. Complete the tables for each function. Compare the designs by finding and comparing average rates of change, minimums, and maximums over the interval [0, 3].
Design A: Design B: y 5x2 5x y 5 5x x y x y 0 0 1 1 2 2 3 3 4 4
Rate of change ______Minimum value on [0, 3] ______Maximum value on [0, 3] ______
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Algebra 1