Math Problem Statement
Solution
The problem asks about the transformations used to change the parent graph of into the graph of the temperature conversion formula . Let's break down the transformations involved.
Given Equation:
Starting with the Parent Graph:
The parent graph is the basic linear function , which is a straight line passing through the origin with a slope of 1.
Step-by-Step Analysis of Transformations:
-
Horizontal Translation:
- The formula contains , which represents a horizontal shift to the right by 32 units. So, the graph is translated horizontally.
-
Vertical Compression:
- The coefficient affects the slope of the line. The original slope of 1 is multiplied by , which compresses the graph vertically (reducing its steepness).
-
No Reflection in the x-axis:
- There is no negative sign multiplying the function, so no reflection across the x-axis occurs.
-
No Vertical Translation:
- There is no constant added or subtracted outside the function, meaning the graph is not shifted vertically.
-
No Reflection in the y-axis:
- Since the -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:
- How does a horizontal translation affect the graph of a linear function?
- What is the effect of vertical compression on a graph’s slope?
- How would the graph change if the slope were negative?
- What are the differences between vertical and horizontal translations?
- How can we identify reflections in the x-axis or y-axis?
Tip:
To identify transformations, always look for changes inside the function (affecting ) for horizontal changes and outside the function for vertical changes (affecting ).
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Math Problem Analysis
Mathematical Concepts
Linear Transformations
Graph Transformations
Formulas
c(x) = 5/9(x - 32)
y = x
Theorems
Transformation of Functions
Horizontal and Vertical Translation
Scaling and Reflection
Suitable Grade Level
Grades 9-11
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