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.








When reflecting a function over the x-axis, you multiply the entire function by \(-1\). 

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

\[
f'(x) = - (3x - 5) = -3x + 5
\]

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

\[
f'(x) = -3x + 5
\]

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.

Given the following equation f(x) = 3x - 5, select the correct equation that shows that the equation reflects over the x-axis.

Learn how to reflect the linear function f(x) = 3x - 5 over the x-axis. This step-by-step guide explains the concept of reflection and how to apply it to the given equation, transforming the function into f'(x) = -3x + 5. Suitable for students in Grades 9-11 studying algebra and function transformations.

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