Q. 5 True or False聽To obtain the gra... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 5 (page 112)

True or False
To obtain the graph of $f (x) = \sqrt{x + 2}$ , shift the graph of $y = \sqrt{x}$ horizontally to the right $2$ units.

Short Answer

Expert verified

False

Step by step solution

Step 1. Concept Used

If the argument $x$ of a function $f$ is replaced by $x - h$ , $h > 0$ , the graph of the new function $y = f (x - h)$ is the graph of $f$ shifted horizontally right $h$ units.

If the argument $x$ of a function $f$ is replaced by $x + h$ , $h > 0$ , the graph of the new function $y = f (x + h)$ is the graph of $f$ shifted horizontally left $h$ units.

Step 2. Identify true or false

As $2$ is added to the argument $x$ of the function $y = \sqrt{x}$ , to get a new function $f (x) = \sqrt{x + 2}$ .

So by the rule horizontal translation the graph of $f (x) = \sqrt{x + 2}$ is obtained by shifting the graph of $y = \sqrt{x}$ horizontally to the left $2$ units.

So the given statement is false.

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91影视

True or False
To obtain the graph of $f (x) = \sqrt{x + 2}$ , shift the graph of $y = \sqrt{x}$ horizontally to the right $2$ units.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Identify true or false

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91影视

True or FalseTo obtain the graph of f(x)=x+2, shift the graph ofy=x horizontally to the right 2units.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Identify true or false

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Discrete Mathematics

Probability and Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

True or False
To obtain the graph of $f (x) = \sqrt{x + 2}$ , shift the graph of $y = \sqrt{x}$ horizontally to the right $2$ units.