let F (x) =(x-4)=1. write a function g whose graph is a vertical shrink of the graph off by a factor of 1/3. G(x)= 

To create a function \( G(x) \) that represents a vertical shrink of the graph of \( F(x) = (x - 4) = 1 \) by a factor of \( \frac{1}{3} \), you need to multiply the output of \( F(x) \) by \( \frac{1}{3} \). This scaling affects the y-values, shrinking them by the given factor.

First, let's rewrite the original equation more clearly:

\[
F(x) = (x - 4) + 1
\]

Now, to apply the vertical shrink by a factor of \( \frac{1}{3} \), you multiply the entire function by \( \frac{1}{3} \):

\[
G(x) = \frac{1}{3} \cdot \left( (x - 4) + 1 \right)
\]

Simplifying this, you get:

\[
G(x) = \frac{1}{3}(x - 4) + \frac{1}{3}
\]

So the new function is:

\[
G(x) = \frac{1}{3}x - \frac{4}{3} + \frac{1}{3}
\]

Further simplifying:

\[
G(x) = \frac{1}{3}x - 1
\]

Thus, the function for the vertical shrink by a factor of \( \frac{1}{3} \) is:

\[
G(x) = \frac{1}{3}x - 1
\]

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the graph of \( G(x) \) change if the vertical shrink factor was \( \frac{1}{2} \) instead of \( \frac{1}{3} \)?
2. What effect would a vertical stretch (e.g., by a factor of 2) have on the function \( F(x) \)?
3. Can you describe how the horizontal shifts affect the original function compared to vertical shifts?
4. What is the difference between vertical and horizontal shrinking in terms of function transformation?
5. How would you find the inverse of the function \( G(x) \)?

**Tip:** When transforming functions, vertical stretches or shrinks multiply the function's output, while horizontal transformations affect the input directly.

let F(x) = (x - 4) = 1. Write a function G whose graph is a vertical shrink of the graph of F by a factor of 1/3. G(x) = 

Learn how to vertically shrink the function F(x) = (x - 4) + 1 by a factor of 1/3. This problem involves function transformations, focusing on scaling in the y-axis. Suitable for students in Grades 9-11, with detailed step-by-step solutions.

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