Explanation Given information : The statement “If f is a function, then f ( 3 x ) = 3 f ( x ) .” Consider the provided statement “If f is a function, then f ( 3 x ) = 3 f ( x ) .” The statement is not true. Counter example: Consider a function f ( x ) = x 2 , Now, take the left hand side of the equation f ( 3 x ) = 3 f ( x ) , substitute the above function to obtain, f ( 3 x ) =

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1, Problem 3TFQ

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To check: Whether the statement “If f is a function, then f(3x)=3f(x) .” is true or false.

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Chapter 1, Problem 2TFQ

Chapter 1, Problem 4TFQ

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Chapter 1 Solutions

Biocalculus

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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To check : Whether the statement “If f is a function, then f ( 3 x ) = 3 f ( x ) .” is true or false.

Solution Summary: The author compares the left and right hand sides of the equation to determine whether the statement "If f is a function" is true.

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To check: Whether the statement “If f is a function, then f(3x)=3f(x) .” is true or false.

Want to see the full answer?

Chapter 1 Solutions