For f(x)=x−6−−−−√�(�)=�−6, what is the vertex of f(x)�(�) after being horizontally dilated by a factor of 22?
Write your answer as an ordered pair. Do not include spaces.

The function given is \( f(x) = \sqrt{x - 6} \).

When a function undergoes a horizontal dilation by a factor of \( k \), the transformation is represented by replacing \( x \) with \( \frac{x}{k} \). So, a horizontal dilation by a factor of 2 modifies the function as follows:

\[
f(x) = \sqrt{\frac{x}{2} - 6}
\]

Now, to find the vertex of this function:

1. The original vertex of \( f(x) = \sqrt{x - 6} \) is at \( (6, 0) \), because the square root function \( \sqrt{x - 6} \) starts at \( x = 6 \) when the expression under the square root equals 0.
   
2. Applying the horizontal dilation by a factor of 2, the new vertex is at \( (2 \times 6, 0) = (12, 0) \).

Thus, the vertex of the transformed function is \( (12,0) \).

### Answer: 
\( (12,0) \)

Would you like more details, or do you have any questions?

Here are five related questions to consider:
1. How does vertical dilation affect the vertex of a function?
2. What happens to the graph of \( f(x) = \sqrt{x - 6} \) if it's shifted vertically?
3. How do you find the domain of a square root function after horizontal dilation?
4. How do horizontal and vertical dilations combine when applied simultaneously to a function?
5. What is the geometric meaning of dilating a function horizontally?

**Tip:** Horizontal dilations affect the \( x \)-coordinates by scaling them, while vertical dilations scale the \( y \)-coordinates.

For f(x)=√(x−6), what is the vertex of f(x) after being horizontally dilated by a factor of 2? Write your answer as an ordered pair. Do not include spaces.

Learn how to find the vertex of the square root function f(x) = √(x - 6) after applying a horizontal dilation by a factor of 2. This solution covers function transformations and the effect of dilations on the vertex. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation