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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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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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

Logic and Functions

Theoretical and Mathematical Physics

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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.