Chapter 9: Q27. (page 594)

Describe how the graph of each function is related to the graph of
$f (x) = x^{2}$ .
$f (x) = \frac{1}{3} x^{2}$

Short Answer

Expert verified

The graph $f (x) = \frac{1}{3} x^{2}$ is the graph vertically compressed from the parent function $f (x) = x^{2}$ .

Step by step solution

Step 1. State the concept.

Vertical Stretch and Vertical Compression:

$y = a f (x), a > 1$ . Sketch the graph $f (x)$ vertically by a factor of a.

$y = a f (x), 0 < a < 1$ . Compress the graph $f (x)$ vertically by a factor of a.

Step 2. Graph each function.

The graph of the functions $f (x) = x^{2}$ and $f (x) = \frac{1}{3} x^{2}$ is given by:

Step 3. State the interpretation of the graph.

The graph of $f (x) = a x^{2}$ stretches or compress the parent graph vertically. Since $a = \frac{1}{3}$ , the graph of $f (x) = \frac{1}{3} x^{2}$ is the graph of $f (x) = x^{2}$ vertically compressed. Compress the graph of $f (x)$ vertically by a factor of $\frac{1}{3}$ .

Therefore, the graph $f (x) = \frac{1}{3} x^{2}$ is the graph of vertically compressed from the parent function $f (x) = x^{2}$ .

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Describe how the graph of each function is related to the graph of
$f (x) = x^{2}$ .
$f (x) = \frac{1}{3} x^{2}$

Short Answer

Step by step solution

Step 1. State the concept.

Step 2. Graph each function.

Step 3. State the interpretation of the graph.

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Short Answer

Step by step solution

Step 1. State the concept.

Step 2. Graph each function.

Step 3. State the interpretation of the graph.

One App. One Place for Learning.

Most popular questions from this chapter

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Describe how the graph of each function is related to the graph of
$f (x) = x^{2}$ .
$f (x) = \frac{1}{3} x^{2}$