Which best describes how the graph of g(x) =1/9sqrt(x) relates to the graph of the parent function, f(x) =sqrt(x) ? The graph of g(x) is shrunk vertically by a factor of 1/9. The graph of g(x) is stretched vertically by a factor of 1/9. The graph of g(x) is shrunk vertically by a factor of 1/3. The graph of g(x) is stretched vertically by a factor of 1/3.

Since we are only modifying a, we are dealing with vertical shrink (a < 1) and stretch (a > 1). Since 1/9 < 1, we have a vertical shrink by a factor of 1/9.

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facundo3141592 facundo3141592 · Answer 2 · 2022-02-17T11:51:27+01:00

The correct description is:

"The graph of g(x) is shrunk vertically by a factor of 1/9"

How do dilations work?

There are two types of dilations.

Vertical dilation:

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x).

Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.

Horizontal dilation:

For a function f(x), a horizontal dilation of scale factor k is wrtten as:

g(x) = f(x/k).

Where if k > 1, we have a dilation, if 0 < k < 1, we have a contraction.

Here we have:

f(x) = √x
g(x) = (1/9)*√x

So we can see that g(x) is a vertical contraction of scale factor 1/9.

Then the correct option is:

"The graph of g(x) is shrunk vertically by a factor of 1/9"

If you want to learn more about dilations, you can read:

https://brainly.com/question/3457976