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The square root parent function is translated so that it has an endpoint located at (4,-1), then
vertically compressed by a factor of 1/3. Write an equation that could represent this function.
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The square root parent function is translated so that it has an endpoint located at 41 then vertically compressed by a factor of 13 Write an equation that could class=

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Answer:

Step-by-step explanation:

[tex]parent~function~f(x)=\sqrt{x-4} -1\\new ~function ~g(x)=\frac{1}{3} \sqrt{x-4}-1[/tex]

Using translation concepts, an equation that could represent this function is:

[tex]f(x) = \frac{1}{3}(\sqrt{x - 4} - 1)[/tex]

The square root parent function is given by:

[tex]f(x) = \sqrt{x}[/tex]

  • The endpoint is (0,0).

What is a translation?

  • A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

After the translation:

  • The endpoint is (4,-1), hence it was shifted 4 units right and 1 unit down, which means that the equation is now:

[tex]f(x) = \sqrt{x + 4} - 1[/tex]

  • Vertically compressed by a factor of [tex]\frac{1}{3}[/tex] means that it was multiplied by [tex]\frac{1}{3}[/tex], hence:

[tex]f(x) = \frac{1}{3}(\sqrt{x - 4} - 1)[/tex]

You can learn more about translation concepts at https://brainly.com/question/4521517