https://file.aiquickdraw.com/mathbot/file/1727316343291cybo23iw.jpg

The question is asking for a translation of the function \( f(x) = \sqrt{x} \).

A translation involves shifting the graph of the function either horizontally, vertically, or both. The problem specifies the following translation:

- **2 units down**: This affects the vertical position of the graph and is represented by subtracting 2 from the function.
- **1 unit to the left**: A leftward horizontal shift is represented by adding 1 to the \( x \)-value.

To apply this translation, the transformed function would be:

\[
f(x) = \sqrt{x} \quad \text{becomes} \quad f(x) = \sqrt{x + 1} - 2
\]

Thus, the translated function is:

\[
f(x) = \sqrt{x + 1} - 2
\]

Would you like further details or have any questions?

Here are five follow-up questions related to this concept:
1. How would the function change if the shift were 3 units to the right and 4 units up?
2. What would be the effect of reflecting the function \( f(x) = \sqrt{x} \) across the x-axis?
3. How does a horizontal stretch or compression affect the function \( f(x) \)?
4. What is the domain of the translated function \( f(x) = \sqrt{x + 1} - 2 \)?
5. How would you graph the function after the translation?

**Tip:** Horizontal shifts affect the \( x \)-values inside the function, while vertical shifts affect the function’s overall output directly.

a translation by 2 units down and 1 unit to the left of f(x) = √x.

Learn how to perform a translation of the function f(x) = √x by 2 units down and 1 unit to the left. This guide covers square root function transformations with a detailed explanation. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation