D¹ = F(x) = 6 - 3x K = ⅓ D² = peregangan secara horizontal h(x) = ?

Given the problem:

- \( D^1 = F(x) = 6 - 3x \) (First function)
- \( K = \frac{1}{3} \) (Horizontal stretch factor)
- \( D^2 = \) (The second function after applying the horizontal stretch)

We need to find the transformed function \( h(x) \).

### Step 1: Understanding the horizontal stretch
A horizontal stretch by a factor of \( K \) is applied to the function \( F(x) \). This transformation affects the input \( x \) by dividing it by \( K \). Mathematically, if \( F(x) \) is the original function, the stretched function \( h(x) \) is given by:

\[
h(x) = F\left(\frac{x}{K}\right)
\]

### Step 2: Applying the stretch to \( F(x) \)
Substitute the value of \( K = \frac{1}{3} \) into the equation:

\[
h(x) = F\left(\frac{x}{\frac{1}{3}}\right) = F(3x)
\]

### Step 3: Substituting \( 3x \) into \( F(x) \)
Given \( F(x) = 6 - 3x \), replace \( x \) with \( 3x \):

\[
h(x) = 6 - 3(3x)
\]

### Step 4: Simplifying the expression
Simplify the expression:

\[
h(x) = 6 - 9x
\]

### Final Answer
The transformed function after the horizontal stretch is:

\[
h(x) = 6 - 9x
\]

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Do you have any questions or need further details? Here are some related questions:

1. What happens if the horizontal stretch factor \( K \) is negative?
2. How does a vertical stretch differ from a horizontal stretch in function transformations?
3. What would be the effect of a horizontal compression instead of a stretch?
4. How can we find the inverse of the function \( F(x) = 6 - 3x \)?
5. How does the graph of \( h(x) = 6 - 9x \) compare to the graph of \( F(x) = 6 - 3x \)?

**Tip:** When dealing with function transformations, always apply the transformation to the variable inside the function before simplifying.

Explore how to apply a horizontal stretch to the linear function F(x) = 6 - 3x with a stretch factor of K = 1/3. This step-by-step guide explains function transformations and simplifies the result to h(x) = 6 - 9x, suitable for Grades 9-11 students.

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