write the equations from a description: the shape of f(x) = sqrt(x), but shifted 6 units to the left and then reflected in both the x-axis and the y-axis

To construct the equation based on your description:

1. **Start with the original function:** \( f(x) = \sqrt{x} \).
2. **Shift the graph 6 units to the left:** Replace \( x \) with \( x + 6 \), so we get \( f(x) = \sqrt{x + 6} \).
3. **Reflect across the x-axis:** Multiply the function by \(-1\), resulting in \( f(x) = -\sqrt{x + 6} \).
4. **Reflect across the y-axis:** Replace \( x \) with \(-x\), resulting in the final function:

\[
f(x) = -\sqrt{-x + 6}
\]

This is the equation for the described transformation of \( f(x) = \sqrt{x} \).

Would you like more details or have any questions? Here are five related questions to deepen understanding:

1. How does shifting a function left or right affect its domain?
2. What happens to the range of \( f(x) \) when it's reflected across the x-axis?
3. How does a reflection across the y-axis impact the behavior of the function?
4. How would a vertical shift influence the shape and position of \( f(x) \)?
5. What are the differences between absolute value transformations and reflections?

**Tip:** When transforming functions, always apply horizontal changes (shifts and reflections) before vertical transformations.

Learn how to transform the function f(x) = sqrt(x) by shifting it 6 units to the left and reflecting it across both the x-axis and the y-axis. This problem covers key concepts in function transformations and reflections. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation