Chapter 9: Q10. (page 597)

Describe how the graph of each function is related to the graph $f (x) = x^{2}$ .
$h (x) = \frac{1}{2} x^{2} + 4$

Short Answer

Expert verified

The graph $h (x) = \frac{1}{2} x^{2} + 4$ is the graph role="math" localid="1647861887784" $f (x) = x^{2}$ vertically compressed by a factor $\frac{1}{2}$ and shifted up 4 4units.

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 $h (x) = \frac{1}{2} x^{2} + 4$ is given by:

Step 3. State the interpretation of the graph.

The function can be written as $f (x) = a x^{2} + c$ , where $a = \frac{1}{2}$ and $c = 4$ .

Note: When $c$ is positive, the graph of a function is translated up and if $c$ is negative, the graph of the function is translated down.

Since $0 < a < 1$ and $c$ is positive, the graph $h (x) = \frac{1}{2} x^{2} + 4$ is the graph $f (x) = x^{2}$ vertically compressed by a factor $\frac{1}{2}$ and shifted up 4 units.

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Describe how the graph of each function is related to the graph $f (x) = x^{2}$ .
$h (x) = \frac{1}{2} x^{2} + 4$

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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Describe how the graph of each function is related to the graphf(x)=x2.h(x)=12x2+4

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

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Mechanics Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Describe how the graph of each function is related to the graph $f (x) = x^{2}$ .
$h (x) = \frac{1}{2} x^{2} + 4$