### Understanding and Writing Function Rules from Graphs#### Instructions:Use the graph to write the function rule. How do you know you are correct?#### Graph Description:The graph plotted here shows a curve which passes through specific points marked in red. The x and y axes are labeled, and the points where the curve intersects the y-axis and x-axis can provide valuable information about the function.1. **Reading Points:** - The graph in this image shows a curve passing through the points (0, 24), (1, 12), and (2, 6).2. **Identifying Function Type:** - The curve suggests an exponential decay function, often represented by the function rule of the form $ y = a \cdot b^x $, where 'a' is a constant and 'b' is the base of the exponent.3. **Determining the Function Rule:** - Given the points provided: - When $ x = 0 $, $ y = 24 $. This tells us that $ a = 24 $ because any number raised to the power of 0 is 1. - When $ x = 1 $, $ y = 12 $. Substituting these values into $ y = a \cdot b^x $ gives us $ 12 = 24 \cdot b $, solving for $ b $, we get $ b = 0.5 $.Therefore, the function rule can be written as:\[ y = 24 \cdot (0.5)^x \]4. **Validation:** - To confirm the rule, substitute $ x = 2 $ into the function $ y = 24 \cdot (0.5)^x $: - $ y = 24 \cdot (0.5)^2 $ - $ y = 24 \cdot 0.25 $ - $ y = 6 $, which matches the point (2, 6) on the graph, confirming our function rule.Using this process of observing points and deriving a consistent function rule allows you to determine the specific function represented by a graph.

Given , We have to use the graph to write the function rule

Answered: 11 Use the graph to write the function…

Math

Algebra

11 Use the graph to write the function rule. How do you know you are correct?

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

### Understanding and Writing Function Rules from Graphs

#### Instructions:
Use the graph to write the function rule. How do you know you are correct?

#### Graph Description:
The graph plotted here shows a curve which passes through specific points marked in red. The x and y axes are labeled, and the points where the curve intersects the y-axis and x-axis can provide valuable information about the function.

1. **Reading Points:**
- The graph in this image shows a curve passing through the points (0, 24), (1, 12), and (2, 6).

2. **Identifying Function Type:**
- The curve suggests an exponential decay function, often represented by the function rule of the form $ y = a \cdot b^x $, where 'a' is a constant and 'b' is the base of the exponent.

3. **Determining the Function Rule:**
- Given the points provided:
- When $ x = 0 $, $ y = 24 $. This tells us that $ a = 24 $ because any number raised to the power of 0 is 1.
- When $ x = 1 $, $ y = 12 $. Substituting these values into $ y = a \cdot b^x $ gives us $ 12 = 24 \cdot b $, solving for $ b $, we get $ b = 0.5 $.

Therefore, the function rule can be written as:
\[ y = 24 \cdot (0.5)^x \]

4. **Validation:**
- To confirm the rule, substitute $ x = 2 $ into the function $ y = 24 \cdot (0.5)^x $:
- $ y = 24 \cdot (0.5)^2 $
- $ y = 24 \cdot 0.25 $
- $ y = 6 $, which matches the point (2, 6) on the graph, confirming our function rule.

Using this process of observing points and deriving a consistent function rule allows you to determine the specific function represented by a graph.

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