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.



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

To apply a horizontal dilation by a factor of 2, we replace \( x \) with \( \frac{x}{2} \). Thus, the new function becomes:

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

Now, let's find the vertex. For the original function, \( f(x) = \sqrt{x - 6} \), the vertex occurs when \( x = 6 \) (since the square root function starts at \( x = 6 \)).

After the horizontal dilation, we need to solve for when the expression inside the square root equals zero:

\[
\frac{x}{2} - 6 = 0
\]

Solving for \( x \):

\[
\frac{x}{2} = 6
\]
\[
x = 12
\]

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

The answer is: \( (12,0) \).

Would you like further details or have any other questions?

Here are 5 related questions:
1. How does horizontal dilation affect the shape of a function?
2. What is the effect of vertical dilation on the vertex of a function?
3. How do you find the domain of a square root function?
4. What changes occur in the graph of a function when both horizontal and vertical dilations are applied?
5. How would you horizontally translate the function \( f(x) = \sqrt{x - 6} \)?

**Tip:** Remember, a horizontal dilation stretches or compresses the graph depending on the factor applied.

For f(x)=sqrt(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 function f(x)=sqrt(x-6) after a horizontal dilation by a factor of 2. This problem demonstrates how to apply transformations to square root functions and identify the new vertex. Suitable for students in Grades 9-11.

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