Math Problem Statement
iven the following equation f left parenthesis x right parenthesis equals 3 x minus 5 , select the correct equation that shows that the equation reflects over the x-axis.
Solution
When reflecting a function over the x-axis, you multiply the entire function by .
Given the original equation , to reflect it over the x-axis, the new function would be:
Thus, the equation that shows the reflection of over the x-axis is:
Would you like any more details or clarifications? Here are 5 related questions to consider:
- How do you reflect a function over the y-axis?
- What happens when you reflect a quadratic function over the x-axis?
- Can you describe how to translate a function vertically or horizontally?
- What is the geometric interpretation of reflecting over the origin?
- How do reflections affect the domain and range of a function?
Tip: When reflecting a function over the x-axis, always apply a negative sign to the entire function.
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Transformation
Reflection
Formulas
f(x) = -[3x - 5] = -3x + 5
Theorems
Reflection over the x-axis theorem
Suitable Grade Level
Grades 9-11
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