QuestionIdentify the parent function for $g(x)=-\sqrt{-x}-8$ and its transformations: reflections, stretches, and shifts.

Studdy Solution

STEP 1

Assumptions1. The function given is $g(x)=-\sqrt{-x}-8$ . We need to identify the parent function from a list of options3. We need to identify the transformations applied to the parent function to obtain the given function

STEP 2

Let's first identify the parent function. The parent function is the simplest form of the given function.Looking at the function $g(x)=-\sqrt{-x}-8$ , we can see that the function involves a square root operation. Therefore, the parent function is $y=\sqrt{x}$ .

STEP 3

Now, let's identify the transformations applied to the parent function to obtain the given function.The negative sign before the square root operation in $g(x)=-\sqrt{-x}-8$ indicates a reflection. Since it's outside the square root, it's a reflection across the x-axis.

STEP 4

The negative sign inside the square root operation in $g(x)=-\sqrt{-x}-8$ indicates another reflection. Since it's inside the square root, it's a reflection across the y-axis.

STEP 5

The "-8" at the end of the function $g(x)=-\sqrt{-x}-8$ indicates a vertical shift. Since it's negative, it's a shift downward by8 units.

STEP 6

There is no multiplication or division by a constant other than1 inside the square root operation, so there is no horizontal stretch or compression.

STEP 7

Similarly, there is no multiplication or division by a constant other than1 outside the square root operation, so there is no vertical stretch or compression.
So, to summarizea) The parent function is $y=\sqrt{x}$ . b) The reflections are across the x-axis and the y-axis. c) There are no stretches or compressions. d) The vertical shift is units downward. e) There is no horizontal shift.

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QuestionIdentify the parent function for $g(x)=-\sqrt{-x}-8$ and its transformations: reflections, stretches, and shifts.

Studdy Solution

STEP 1

Assumptions1. The function given is $g(x)=-\sqrt{-x}-8$ . We need to identify the parent function from a list of options3. We need to identify the transformations applied to the parent function to obtain the given function

STEP 2

Let's first identify the parent function. The parent function is the simplest form of the given function.Looking at the function $g(x)=-\sqrt{-x}-8$ , we can see that the function involves a square root operation. Therefore, the parent function is $y=\sqrt{x}$ .

STEP 3

Now, let's identify the transformations applied to the parent function to obtain the given function.The negative sign before the square root operation in $g(x)=-\sqrt{-x}-8$ indicates a reflection. Since it's outside the square root, it's a reflection across the x-axis.

STEP 4

The negative sign inside the square root operation in $g(x)=-\sqrt{-x}-8$ indicates another reflection. Since it's inside the square root, it's a reflection across the y-axis.

STEP 5

The "-8" at the end of the function $g(x)=-\sqrt{-x}-8$ indicates a vertical shift. Since it's negative, it's a shift downward by8 units.

STEP 6

There is no multiplication or division by a constant other than1 inside the square root operation, so there is no horizontal stretch or compression.

STEP 7

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QuestionIdentify the parent function for g(x)=−−x−8g(x)=-\sqrt{-x}-8g(x)=−−x​−8 and its transformations: reflections, stretches, and shifts.

Studdy Solution

STEP 1

Assumptions1. The function given is g(x)=−−x−8g(x)=-\sqrt{-x}-8g(x)=−−x​−8 . We need to identify the parent function from a list of options3. We need to identify the transformations applied to the parent function to obtain the given function

STEP 2

STEP 3

STEP 4

The negative sign inside the square root operation in g(x)=−−x−8g(x)=-\sqrt{-x}-8g(x)=−−x​−8 indicates another reflection. Since it's inside the square root, it's a reflection across the y-axis.

STEP 5

The "-8" at the end of the function g(x)=−−x−8g(x)=-\sqrt{-x}-8g(x)=−−x​−8 indicates a vertical shift. Since it's negative, it's a shift downward by8 units.

STEP 6

There is no multiplication or division by a constant other than1 inside the square root operation, so there is no horizontal stretch or compression.

STEP 7

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the parent function for $g(x)=-\sqrt{-x}-8$ and its transformations: reflections, stretches, and shifts.

Assumptions1. The function given is $g(x)=-\sqrt{-x}-8$ . We need to identify the parent function from a list of options3. We need to identify the transformations applied to the parent function to obtain the given function

The negative sign inside the square root operation in $g(x)=-\sqrt{-x}-8$ indicates another reflection. Since it's inside the square root, it's a reflection across the y-axis.

The "-8" at the end of the function $g(x)=-\sqrt{-x}-8$ indicates a vertical shift. Since it's negative, it's a shift downward by8 units.