Math Problem Statement
Assume that (a, b) is a point on the graph of f. What is the corresponding point on the graph of the following function?
yequals=f left parenthesis negative x right parenthesis
Solution
When dealing with the transformation , you are reflecting the graph of over the -axis. This means that for every point on the graph of , the corresponding point on the graph of will be .
Explanation:
- The function takes the input and negates it before applying the function .
- If is on the graph of , then .
- For , you replace with in the function, so .
- Thus, the point on the graph of corresponds to the point on the graph of .
So, the corresponding point on the graph of is .
Would you like further clarification on any aspect of this transformation or have any additional questions?
Related Questions:
- What is the effect on the graph of when applying the transformation ?
- How does the transformation affect the graph of ?
- What happens to the graph of if the transformation is applied?
- If , how is the graph of affected?
- What point corresponds to on the graph of ?
Tip:
When dealing with transformations of functions, visualize how each change (reflection, shift, stretch, etc.) affects the graph. This approach can help you determine the corresponding points and understand the overall transformation better.
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Math Problem Analysis
Mathematical Concepts
Function transformations
Reflections over the y-axis
Formulas
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Theorems
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Suitable Grade Level
High School