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 1-1.

Given the original equation f(x)=3x5f(x) = 3x - 5, to reflect it over the x-axis, the new function would be:

f(x)=(3x5)=3x+5f'(x) = - (3x - 5) = -3x + 5

Thus, the equation that shows the reflection of f(x)f(x) over the x-axis is:

f(x)=3x+5f'(x) = -3x + 5

Would you like any more details or clarifications? Here are 5 related questions to consider:

  1. How do you reflect a function over the y-axis?
  2. What happens when you reflect a quadratic function over the x-axis?
  3. Can you describe how to translate a function vertically or horizontally?
  4. What is the geometric interpretation of reflecting over the origin?
  5. 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