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The problem asks about the transformations used to change the parent graph of \( y = x \) into the graph of the temperature conversion formula \( c(x) = \frac{5}{9}(x - 32) \). Let's break down the transformations involved.

### Given Equation: 
\[ c(x) = \frac{5}{9}(x - 32) \]

### Starting with the Parent Graph:
The parent graph is the basic linear function \( y = x \), which is a straight line passing through the origin with a slope of 1.

### Step-by-Step Analysis of Transformations:
1. **Horizontal Translation**: 
   - The formula contains \( (x - 32) \), which represents a horizontal shift to the right by 32 units. So, the graph is translated horizontally.
   
2. **Vertical Compression**: 
   - The coefficient \( \frac{5}{9} \) affects the slope of the line. The original slope of 1 is multiplied by \( \frac{5}{9} \), which compresses the graph vertically (reducing its steepness).
   
3. **No Reflection in the x-axis**: 
   - There is no negative sign multiplying the function, so no reflection across the x-axis occurs.
   
4. **No Vertical Translation**: 
   - There is no constant added or subtracted outside the function, meaning the graph is not shifted vertically.
   
5. **No Reflection in the y-axis**: 
   - Since the \( x \)-term remains positive, there is no reflection across the y-axis.

### Conclusion:
The correct transformations are:
- Horizontal translation
- Vertical compression

### Do you want further details or clarifications?

### Here are 5 related questions:
1. How does a horizontal translation affect the graph of a linear function?
2. What is the effect of vertical compression on a graph’s slope?
3. How would the graph change if the slope were negative?
4. What are the differences between vertical and horizontal translations?
5. How can we identify reflections in the x-axis or y-axis?

### Tip:
To identify transformations, always look for changes inside the function (affecting \( x \)) for horizontal changes and outside the function for vertical changes (affecting \( y \)).

What transformations are used in transforming the parent graph y = x to obtain the graph of c(x) = 5/9(x - 32)?

Explore the transformations needed to convert the graph of y = x into the graph for the Celsius temperature formula c(x) = 5/9(x - 32). Learn about horizontal translation, vertical compression, and other key linear graph transformations suitable for Grades 9-11.

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