Explanation Given: The function is f ( x ) = | x | + 1 . a. y = f ( x − 1 ) b. y = − f ( x ) c. y = − f ( x ) + 2 d. y = f ( x − 1 ) − 2 e. y = f ( x + 1 ) Calculation: Part a: Find the points to draw the graph of the function y = f ( x − 1 ) . The given function is f ( x ) = | x | + 1 . Substitute x − 1 in place of x . f ( x − 1 ) = | x − 1 | + 1 We can rewrite it as: y = | x − 1 | + 1 Put x = − 2 in the given function. y = | ( − 2 ) − 1 | + 1 = 3 + 1 = 4 Put x = − 1 in the given function. y = | ( − 1 ) − 1 | + 1 = 2 + 1 = 3 Put x = 0 in the given function. y = | 0 − 1 | + 1 = 1 + 1 = 2 Put x = 1 in the given function. y = | 1 − 1 | + 1 = 0 + 1 = 1 Put x = 2 in the given function. y = | 2 − 1 | + 1 = 1 + 1 = 2 The points are: x − 2 − 1 0 1 2 y 4 3 2 1 2 The graph is: Hence, the graph of option (a) is (v). Part b: Find the points to draw the graph of the function y = − f ( x ) . The given function is f ( x ) = | x | + 1 . Multiply with ( − ) of the above function. − f ( x ) = − ( | x | + 1 ) We can rewrite it as: y = − ( | x | + 1 ) Put x = − 2 in the given function. y = − ( | − 2 | + 1 ) = − ( 3 ) = − 3 Put x = − 1 in the given function. y = − ( | − 1 | + 1 ) = − ( 2 ) = − 2 Put x = 0 in the given function. y = − ( | 0 | + 1 ) = − ( 1 ) = − 1 Put x = 1 in the given function. y = − ( | 1 | + 1 ) = − ( 2 ) = − 2 Put x = 2 in the given function. y = − ( | 2 | + 1 ) = − ( 3 ) = − 3 The points are: x − 2 − 1 0 1 2 y − 3 − 2 − 1 − 2 − 3 The graph is: Hence, the graph of option (b) is (iv). Part c: Find the points to draw the graph of the function y = − f ( x ) + 2 . The given function is f ( x ) = | x | + 1 . Multiply with ( − ) of the above function. − f ( x ) = − ( | x | + 1 ) Add 2 on both sides. − f ( x ) + 2 = − | x | − 1 + 2 = − | x | + 1 We can rewrite it as: y = − | x | + 1 Put x = − 2 in the given function. y = − | x | + 1 = − | − 2 | + 1 = − 1 Put x = − 1 in the given function

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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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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Question

Chapter 1.1, Problem 80E

To determine

Match the functions (a)-(e) with their graphs (i)-(v).

a. y=f(x−1)

b. y=−f(x)

c. y=−f(x)+2

d. y=f(x−1)−2

e. y=f(x+1)

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Chapter 1.1, Problem 79E

Chapter 1.1, Problem 81E

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Chapter 1 Solutions

CALCULUS (CLOTH)

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

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 Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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Prob. 33CRE Ch. 1 - Prob. 34CRE Ch. 1 - Prob. 35CRE Ch. 1 - Prob. 36CRE Ch. 1 - Prob. 37CRE Ch. 1 - Prob. 38CRE Ch. 1 - Prob. 39CRE Ch. 1 - Prob. 40CRE Ch. 1 - Prob. 41CRE Ch. 1 - Prob. 42CRE Ch. 1 - Prob. 43CRE Ch. 1 - Prob. 44CRE Ch. 1 - Prob. 45CRE Ch. 1 - Prob. 46CRE Ch. 1 - Prob. 47CRE Ch. 1 - Prob. 48CRE Ch. 1 - Prob. 49CRE Ch. 1 - Prob. 50CRE Ch. 1 - Prob. 51CRE Ch. 1 - Prob. 52CRE Ch. 1 - Prob. 53CRE Ch. 1 - Prob. 54CRE

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Match the functions (a)-(e) with their graphs (i)-(v). a. y = f ( x − 1 ) b. y = − f ( x ) c. y = − f ( x ) + 2 d. y = f ( x − 1 ) − 2 e. y = f ( x + 1 )

Solution Summary: The author explains how to draw the graph of the function y=f(x-1).

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Videos

Match the functions (a)-(e) with their graphs (i)-(v).

a. y=f(x−1)

b. y=−f(x)

c. y=−f(x)+2

d. y=f(x−1)−2

e. y=f(x+1)

Want to see the full answer?

Chapter 1 Solutions

Match the functions (a)-(e) with their graphs (i)-(v). a. y = f ( x − 1 ) b. y = − f ( x ) c. y = − f ( x ) + 2 d. y = f ( x − 1 ) − 2 e. y = f ( x + 1 )

Solution Summary: The author explains how to draw the graph of the function y=f(x-1).

Concept explainers

Videos

Match the functions (a)-(e) with their graphs (i)-(v). a. y=f(x−1) b. y=−f(x) c. y=−f(x)+2 d. y=f(x−1)−2 e. y=f(x+1)

Want to see the full answer?

Chapter 1 Solutions

Match the functions (a)-(e) with their graphs (i)-(v).

a. y=f(x−1)

b. y=−f(x)

c. y=−f(x)+2

d. y=f(x−1)−2

e. y=f(x+1)