Q. 501 In the following exercises, grap... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 501 (page 986)

In the following exercises, graph each function using a horizontal shift.
$g (x) = {(x - 3)}^{2}$

Short Answer

Expert verified

The graph of the function is shown below:

Step by step solution

Step 1. Given information.

We have:

$g (x) = {(x - 3)}^{2}$

Step 2. Find the points lying on the function.

The parent function of the given function $g (x) = {(x - 3)}^{2}$ is $f (x) = x^{2}$ .

Note that the graph of $g (x)$ is simply a horizontal translation by three to the right of the graph of $f (x) .$

Therefore by translating the graph of $f (x) = x^{2}$ by three units to the right, the graph of $g (x) = {(x - 3)}^{2}$ is obtained.

Evaluate $f (x) = x^{2}$ for $x = - 2$ .

$f (x) = x^{2}, x = - 2 f (- 2) = {(- 2)}^{2} = 4 f (x) = x^{2}, x = 0 f (0) = {(0)}^{2} = 4 f (x) = x^{2}, x = 2 f (2) = {(2)}^{2} = 4$

Therefore, the following points lie on the graph of $f (x) = x^{2}$ :

$(- 2, 4), (0, 0), (2, 4)$

Step 3. Plot the points and draw the graph.

Plot the points $(- 2, 0), (0, 0), (2, 4)$ on the graph.

Draw a smooth curve in the shape of a parabola through the plotted points to obtain the graph of $f (x) = x^{2}$ .

Shift the graph of $f (x) = x^{2}$ by $3$ units to the right to obtain the graph of $g (x) = {(x - 3)}^{2}$ .

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91影视

In the following exercises, graph each function using a horizontal shift.
$g (x) = {(x - 3)}^{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the points lying on the function.

Step 3. Plot the points and draw the graph.

One App. One Place for Learning.

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91影视

In the following exercises, graph each function using a horizontal shift.g(x)=x-32

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the points lying on the function.

Step 3. Plot the points and draw the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Geometry

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each function using a horizontal shift.
$g (x) = {(x - 3)}^{2}$