Chapter 2: Q. 1 (page 112)

Suppose that the graph of a function f is known. Then the graph of $y = f (x - 2)$ may be obtained by a(n) shift of the graph of $f$ to the a distance of $2$ units.

Short Answer

Expert verified

horizontal; right

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. Fill in the blanks

When the argument $x$ of a function $f$ is replaced by $x - 2$ , then the new function $y = f (x - 2)$ is the graph of $f$ shifted horizontally right $2$ units.

So if the graph of a function $f$ is known. Then the graph of $y = f (x - 2)$ may be obtained by a horizontal shift of the graph of $f$ to the right a distance of $2$ units.

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Suppose that the graph of a function f is known. Then the graph of $y = f (x - 2)$ may be obtained by a(n) shift of the graph of $f$ to the a distance of $2$ units.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Fill in the blanks

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Suppose that the graph of a function f is known. Then the graph of y=f(x-2)may be obtained by a(n) ________ shift of the graph of f to the ________ a distance of2 units.

Short Answer

Step by step solution

Step 1. Concept Used

Step 2. Fill in the blanks

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Suppose that the graph of a function f is known. Then the graph of $y = f (x - 2)$ may be obtained by a(n) shift of the graph of $f$ to the a distance of $2$ units.