QuestionDetermine the final function after shifting $y=\sqrt{x}$ up 9 units, reflecting it about the $y$ axis, and shifting left 3 units.

Studdy Solution

STEP 1

Assumptions1. The original function is $y=\sqrt{x}$ . The transformations are applied in the following order a. Shift up9 units b. Reflect about the y-axis c. Shift left3 units

STEP 2

First, let's apply the first transformation to the original function. A shift up by9 units means we add9 to the function.
$y = \sqrt{x} +9$

STEP 3

Next, let's apply the second transformation. A reflection about the y-axis means we replace $x$ with $-x$ in the function.
$y = \sqrt{-x} +9$

STEP 4

Finally, let's apply the third transformation. A shift to the left by3 units means we replace $x$ with $(x+3)$ in the function.
$y = \sqrt{-(x+3)} +9$

STEP 5

implify the function.
$y = \sqrt{-x-3} +9$ So, the function that is finally graphed after the transformations is $y = \sqrt{-x-3} +9$ .

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QuestionDetermine the final function after shifting $y=\sqrt{x}$ up 9 units, reflecting it about the $y$ axis, and shifting left 3 units.

Studdy Solution

STEP 1

Assumptions1. The original function is $y=\sqrt{x}$ . The transformations are applied in the following order a. Shift up9 units b. Reflect about the y-axis c. Shift left3 units

STEP 2

First, let's apply the first transformation to the original function. A shift up by9 units means we add9 to the function.
$y = \sqrt{x} +9$

STEP 3

Next, let's apply the second transformation. A reflection about the y-axis means we replace $x$ with $-x$ in the function.
$y = \sqrt{-x} +9$

STEP 4

Finally, let's apply the third transformation. A shift to the left by3 units means we replace $x$ with $(x+3)$ in the function.
$y = \sqrt{-(x+3)} +9$

STEP 5

implify the function.
$y = \sqrt{-x-3} +9$ So, the function that is finally graphed after the transformations is $y = \sqrt{-x-3} +9$ .

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QuestionDetermine the final function after shifting y=xy=\sqrt{x}y=x​ up 9 units, reflecting it about the yyy axis, and shifting left 3 units.

Studdy Solution

STEP 1

Assumptions1. The original function is y=xy=\sqrt{x}y=x​ . The transformations are applied in the following order a. Shift up9 units b. Reflect about the y-axis c. Shift left3 units

STEP 2

First, let's apply the first transformation to the original function. A shift up by9 units means we add9 to the function.y=x+9y = \sqrt{x} +9y=x​+9

STEP 3

Next, let's apply the second transformation. A reflection about the y-axis means we replace xxx with −x-x−x in the function.y=−x+9y = \sqrt{-x} +9y=−x​+9

STEP 4

Finally, let's apply the third transformation. A shift to the left by3 units means we replace xxx with (x+3)(x+3)(x+3) in the function.y=−(x+3)+9y = \sqrt{-(x+3)} +9y=−(x+3)​+9

STEP 5

implify the function.y=−x−3+9y = \sqrt{-x-3} +9y=−x−3​+9So, the function that is finally graphed after the transformations is y=−x−3+9y = \sqrt{-x-3} +9y=−x−3​+9.

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QuestionDetermine the final function after shifting $y=\sqrt{x}$ up 9 units, reflecting it about the $y$ axis, and shifting left 3 units.

Assumptions1. The original function is $y=\sqrt{x}$ . The transformations are applied in the following order a. Shift up9 units b. Reflect about the y-axis c. Shift left3 units

First, let's apply the first transformation to the original function. A shift up by9 units means we add9 to the function.
$y = \sqrt{x} +9$

Next, let's apply the second transformation. A reflection about the y-axis means we replace $x$ with $-x$ in the function.
$y = \sqrt{-x} +9$

Finally, let's apply the third transformation. A shift to the left by3 units means we replace $x$ with $(x+3)$ in the function.
$y = \sqrt{-(x+3)} +9$

implify the function.
$y = \sqrt{-x-3} +9$ So, the function that is finally graphed after the transformations is $y = \sqrt{-x-3} +9$ .