The image shows an online educational tool for learning about exponential functions. The section is titled "Graphs, Functions, and Systems" with a focus on creating a "Table for an Exponential Function."**Table Structure:**- Two columns labeled \( x \) and \( h(x) \).- Five rows for the values: - \( x = -2 \) - \( x = -1 \) - \( x = 0 \) - \( x = 1 \) - \( x = 2 \)- Each row has an empty box next to \( h(x) \), indicating that students are expected to fill in the values of the exponential function for each corresponding \( x \).**Interface Features:**- Buttons at the top-right corner of the table allowing for actions such as resetting entries.- Below the table, there are options to get "Explanation" or to "Check" the answers input into the table.This interactive element is designed to help students understand how exponential functions behave and how their values are calculated for different inputs. **Educational Content: Evaluating Exponential Functions****The function** \( h \) **is defined by the following rule:**\[ h(x) = \left(\frac{1}{5}\right)^x \]**Objective: Find** \( h(x) \) **for each** \( x \)-**value in the table.****Table Values:**\[\begin{array}{|c|c|}\hlinex & h(x) \\\hline-2 & \_ \\-1 & \_ \\0 & \_ \\1 & \_ \\\hline\end{array}\]**Instructions:**1. Evaluate the function \( h(x) = \left(\frac{1}{5}\right)^x \) for each value of \( x \) listed in the table.2. Fill in the blanks with the calculated values of \( h(x) \).**Steps for Calculation:**- **For \( x = -2 \):** Compute \( h(-2) = \left(\frac{1}{5}\right)^{-2} = 5^2 = 25 \)- **For \( x = -1 \):** Compute \( h(-1) = \left(\frac{1}{5}\right)^{-1} = 5 \)- **For \( x = 0 \):** Compute \( h(0) = \left(\frac{1}{5}\right)^0 = 1 \)- **For \( x = 1 \):** Compute \( h(1) = \left(\frac{1}{5}\right)^1 = \frac{1}{5} = 0.2 \)**Fill in the Table:**\[\begin{array}{|c|c|}\hlinex & h(x) \\\hline-2 & 25 \\-1 & 5 \\0 & 1 \\1 & 0.2 \\\hline\end{array}\]**Interactive Feature:**The diagram to the right of the table appears to be a control panel with two selectable options and a reset button, likely used for interactive learning exercises or entering values. Use the provided tools to input your solutions and verify correctness.

Answered: Image /qna-images/answer/be64ae4e-c022-4f57-b5f2-db6254120881.jpg

Answered: The function h is defined by the…

Math

Algebra

The function h is defined by the following rule. X n(x) = (1/3 (;}) Find h(x) for each x-value in the table.

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

The image shows an online educational tool for learning about exponential functions. The section is titled "Graphs, Functions, and Systems" with a focus on creating a "Table for an Exponential Function."

**Table Structure:**

- Two columns labeled \( x \) and \( h(x) \).
- Five rows for the values:

- \( x = -2 \)
- \( x = -1 \)
- \( x = 0 \)
- \( x = 1 \)
- \( x = 2 \)

- Each row has an empty box next to \( h(x) \), indicating that students are expected to fill in the values of the exponential function for each corresponding \( x \).

**Interface Features:**

- Buttons at the top-right corner of the table allowing for actions such as resetting entries.
- Below the table, there are options to get "Explanation" or to "Check" the answers input into the table.

This interactive element is designed to help students understand how exponential functions behave and how their values are calculated for different inputs.

**Educational Content: Evaluating Exponential Functions**

**The function** \( h \) **is defined by the following rule:**

\[ h(x) = \left(\frac{1}{5}\right)^x \]

**Objective: Find** \( h(x) \) **for each** \( x \)-**value in the table.**

**Table Values:**

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

**Instructions:**

1. Evaluate the function \( h(x) = \left(\frac{1}{5}\right)^x \) for each value of \( x \) listed in the table.
2. Fill in the blanks with the calculated values of \( h(x) \).

**Steps for Calculation:**

- **For \( x = -2 \):** Compute \( h(-2) = \left(\frac{1}{5}\right)^{-2} = 5^2 = 25 \)
- **For \( x = -1 \):** Compute \( h(-1) = \left(\frac{1}{5}\right)^{-1} = 5 \)
- **For \( x = 0 \):** Compute \( h(0) = \left(\frac{1}{5}\right)^0 = 1 \)
- **For \( x = 1 \):** Compute \( h(1) = \left(\frac{1}{5}\right)^1 = \frac{1}{5} = 0.2 \)

**Fill in the Table:**

\[
\begin{array}{|c|c|}
\hline
x & h(x) \\
\hline
-2 & 25 \\
-1 & 5 \\
0 & 1 \\
1 & 0.2 \\
\hline
\end{array}
\]

**Interactive Feature:**

The diagram to the right of the table appears to be a control panel with two selectable options and a reset button, likely used for interactive learning exercises or entering values. Use the provided tools to input your solutions and verify correctness.

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