The function
f
(
x
)
=
x
is vertically compressed to
1
5
of its height. The point
(
1
,
1
)
is transformed to become what point?

The function \( f(x) = x \) is transformed by vertically compressing it to \(\frac{1}{5}\) of its height. 

Vertical compression affects the \( y \)-coordinate of the points on the graph. Specifically, the \( y \)-coordinates are multiplied by the compression factor. 

Given that the original function is \( f(x) = x \), the point \( (1, 1) \) lies on this function.

When the function is compressed vertically by a factor of \(\frac{1}{5}\), the new function can be represented as:

\[
g(x) = \frac{1}{5}f(x) = \frac{1}{5}x
\]

Now, applying this transformation to the point \( (1, 1) \):

- The \( x \)-coordinate remains unchanged: \( x = 1 \).
- The \( y \)-coordinate is multiplied by \(\frac{1}{5}\): \( y = \frac{1}{5} \times 1 = \frac{1}{5} \).

So, the point \( (1, 1) \) is transformed to \( \left(1, \frac{1}{5}\right) \).

### Summary:
The point \( (1, 1) \) is transformed to \( \left(1, \frac{1}{5}\right) \).

Would you like more details or have any questions? 

Here are five related questions:

1. What happens to the point \( (2, 4) \) under the same transformation?
2. How would the function change if it were stretched instead of compressed?
3. What is the effect of horizontal compression on a linear function?
4. How does a vertical shift affect the graph of \( f(x) = x \)?
5. What is the transformation formula for a vertical stretch by a factor of 3?

**Tip:** When dealing with vertical transformations, remember that they only affect the \( y \)-coordinates of the points on the graph.

Explore how the function f(x) = x is vertically compressed to 1/5 of its height, transforming the point (1, 1) to (1, 1/5). Understand the impact of vertical compression on function graphs and coordinate transformations.

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The function f ( x )

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