### Function TransformationsThe following tables provide the values of the functions \( f \), \( g \), and \( h \) for specific values of \( x \). Your task is to express \( g(x) \) and \( h(x) \) as transformations of \( f(x) \).#### Function \( f \)\[\begin{array}{|c|c|c|c|c|c|}\hlinex & -2 & -1 & 0 & 1 & 2 \\\hlinef(x) & -2 & -1 & -3 & 1 & 2 \\\hline\end{array}\]#### Function \( g \)\[\begin{array}{|c|c|c|c|c|c|}\hlinex & -3 & -2 & -1 & 0 & 1 \\\hlineg(x) & -2 & -1 & -3 & 1 & 2 \\\hline\end{array}\]#### Function \( h \)\[\begin{array}{|c|c|c|c|c|c|}\hlinex & -2 & -1 & 0 & 1 & 2 \\\hlineh(x) & 0 & 1 & -1 & 3 & 4 \\\hline\end{array}\]### TransformationsTo determine the transformations:1. **For \( g(x) \):** - Notice how the values of \( g(x) \) match those of \( f(x) \) for different \( x \) values. - You will need to identify the transformation that maps \( x\) to the new \( x \)-values in the table for \( g(x) \).2. **For \( h(x) \):** - Compare the values of \( h(x) \) with those of \( f(x) \). - Identify how \( f(x)\) is altered (translated, stretched, reflected, etc.) to match the values of \( h(x) \).Use the space below to enter the transformations of \( f(x) \):\ \( g(x) =\)

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Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x). 2 x 1 0 1 2 f(x) 2 - 1 1 2 -3 -2 0 1 - 2 - 1 1 2 - 2 1 2 0 3 4 g(x) = h(x) = 8 g(x) X h (x) AJ 45 Ay A₂ 1 1 3 -1 3 0 -1

Tabular representations for the functions f, g, and h are given below. Write g(x) and h(x) as transformations of f(x). 2 x 1 0 1 2 f(x) 2 - 1 1 2 -3 -2 0 1 - 2 - 1 1 2 - 2 1 2 0 3 4 g(x) = h(x) = 8 g(x) X h (x) AJ 45 Ay A₂ 1 1 3 -1 3 0 -1

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Function Transformations

The following tables provide the values of the functions \( f \), \( g \), and \( h \) for specific values of \( x \). Your task is to express \( g(x) \) and \( h(x) \) as transformations of \( f(x) \).

#### Function \( f \)

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -2 & -1 & 0 & 1 & 2 \\
\hline
f(x) & -2 & -1 & -3 & 1 & 2 \\
\hline
\end{array}
\]

#### Function \( g \)

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -3 & -2 & -1 & 0 & 1 \\
\hline
g(x) & -2 & -1 & -3 & 1 & 2 \\
\hline
\end{array}
\]

#### Function \( h \)

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & -2 & -1 & 0 & 1 & 2 \\
\hline
h(x) & 0 & 1 & -1 & 3 & 4 \\
\hline
\end{array}
\]

### Transformations

To determine the transformations:

1. **For \( g(x) \):**
- Notice how the values of \( g(x) \) match those of \( f(x) \) for different \( x \) values.
- You will need to identify the transformation that maps \( x\) to the new \( x \)-values in the table for \( g(x) \).

2. **For \( h(x) \):**
- Compare the values of \( h(x) \) with those of \( f(x) \).
- Identify how \( f(x)\) is altered (translated, stretched, reflected, etc.) to match the values of \( h(x) \).

Use the space below to enter the transformations of \( f(x) \):

\<form>
\( g(x) =\) <input type="text" name="g_transformation"> <br><br>

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