Chapter 9: Q26. (page 594)

Describe how the graph of each function is related to the graph of
$f (x) = x^{2}$ .
$f (x) = 4 x^{2} - 18$

Short Answer

Expert verified

The graph $f (x) = 4 x^{2} - 18$ is the graph of $f (x) = x^{2}$ translated 18 units down and stretches vertically by a factor 4.

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 $f (x) = 4 x^{2} - 18$ is given by:

Step 3. State the interpretation of the graph.

The graph of $f (x) = a x^{2} + c$ stretches or compress the parent graph $f (x) = x^{2}$ vertically and translated up or down.

If $|a| > 1$ , stretch the graph $f (x)$ vertically by a factor of $|a|$ . Since $a = 4$ , the graph of $f (x) = 4 x^{2} - 18$ is the graph of $f (x) = x^{2}$ vertically stretched by a factor 5. It $c$ is positive, then translated up and if $c$ is negative, then translated down. $c = - 18$ , translated 18 units down.

Therefore, the graph $f (x) = 4 x^{2} - 18$ is the graph of $f (x) = x^{2}$ translated 18 units down and stretches vertically by a factor 4.

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Describe how the graph of each function is related to the graph of
$f (x) = x^{2}$ .
$f (x) = 4 x^{2} - 18$

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 graph off(x)=x2.f(x)=4x2−18

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

Discrete Mathematics

Logic and Functions

Applied Mathematics

Mechanics Maths

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Describe how the graph of each function is related to the graph of
$f (x) = x^{2}$ .
$f (x) = 4 x^{2} - 18$