Explanation Given information: The table x f ( x ) g ( x ) h ( x ) -2 12 16 37 -1 17 24 34 0 20 36 31 1 21 54 28 2 18 81 25 Concept Involved: Linear function: Linear functions graph as a straight line, no curves allowed. So, if the graph is a straight line, it is the graph of a linear function. From a table, you can verify a linear function by examining the x and y values. The rate of change for y with respect to x remains constant for a linear function. This rate of change is called the slope. The linear function will be in the form y = m ︷ S l o p e ⋅ x + b ︷ y − i n t e r c e p t where m is the slope and b is the y-intercept. Calculation: Steps Description m = y 2 − y 1 x 2 − x 1 = 17 − 12 − 1 − ( − 2 ) = 5 1 = 5 m = y 3 − y 2 x 3 − x 2 = 20 − 17 0 − ( − 1 ) = 3 1 = 3 S i n c e m = y 2 − y 1 x 2 − x 1 ≠ y 3 − y 2 x 3 − x 2 it proves that table does not have constant rate of change (slope) so table does not have the characteristics that y could be a linear function of x Checking whether function f(x) from the table have constant rate of change m = y 2 − y 1 x 2 − x 1 = 24 − 16 − 1 − ( − 2 ) = 8 1 = To determine (b) To check: Whether there is any function from the given table that could be exponential and formula for the same.

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 1.5, Problem 35P

To determine

(a)

To check:

Whether there is any function from the given table that could be linear and formula for the same.

To determine

(b)

To check:

Whether there is any function from the given table that could be exponential and formula for the same.

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Chapter 1.5, Problem 34P

Chapter 1.5, Problem 36P

Chapter 1 Solutions

APPLIED CALCULUS-WILEYPLUS

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(a) To check: Whether there is any function from the given table that could be linear and formula for the same.

Solution Summary: The author explains that linear functions graph as a straight line, no curves allowed. The rate of change for y with respect to x is called the slope.