Math / Algebra

QuestionWrite the function whose graph is the graph of $y=\sqrt{x}$ but is shifted down 3 units. $\mathrm{y}=\square$

Studdy Solution

STEP 1

1. The original function is $y = \sqrt{x}$ .
2. The transformation involves shifting the graph down by 3 units.

STEP 2

1. Understand the effect of shifting a graph vertically.
2. Apply the transformation to the original function.
3. Write the new function.

STEP 3

A vertical shift downwards by 3 units means we subtract 3 from the original function's output.

STEP 4

To shift the graph of $y = \sqrt{x}$ down by 3 units, we modify the function to $y = \sqrt{x} - 3$ .

STEP 5

The new function, after applying the vertical shift, is:
$y = \sqrt{x} - 3$
The function whose graph is the graph of $y = \sqrt{x}$ but shifted down 3 units is:
$\boxed{y = \sqrt{x} - 3}$

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QuestionWrite the function whose graph is the graph of $y=\sqrt{x}$ but is shifted down 3 units. $\mathrm{y}=\square$

Studdy Solution

STEP 1

1. The original function is $y = \sqrt{x}$ .
2. The transformation involves shifting the graph down by 3 units.

STEP 2

1. Understand the effect of shifting a graph vertically.
2. Apply the transformation to the original function.
3. Write the new function.

STEP 3

A vertical shift downwards by 3 units means we subtract 3 from the original function's output.

STEP 4

To shift the graph of $y = \sqrt{x}$ down by 3 units, we modify the function to $y = \sqrt{x} - 3$ .

STEP 5

The new function, after applying the vertical shift, is:
$y = \sqrt{x} - 3$
The function whose graph is the graph of $y = \sqrt{x}$ but shifted down 3 units is:
$\boxed{y = \sqrt{x} - 3}$

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QuestionWrite the function whose graph is the graph of y=xy=\sqrt{x}y=x​ but is shifted down 3 units. y=□\mathrm{y}=\squarey=□

Studdy Solution

STEP 1

1. The original function is y=x y = \sqrt{x} y=x​.2. The transformation involves shifting the graph down by 3 units.

STEP 2

1. Understand the effect of shifting a graph vertically.2. Apply the transformation to the original function.3. Write the new function.

STEP 3

A vertical shift downwards by 3 units means we subtract 3 from the original function's output.

STEP 4

To shift the graph of y=x y = \sqrt{x} y=x​ down by 3 units, we modify the function to y=x−3 y = \sqrt{x} - 3 y=x​−3.

STEP 5

The new function, after applying the vertical shift, is:y=x−3 y = \sqrt{x} - 3 y=x​−3 The function whose graph is the graph of y=x y = \sqrt{x} y=x​ but shifted down 3 units is:y=x−3 \boxed{y = \sqrt{x} - 3} y=x​−3​

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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.

QuestionWrite the function whose graph is the graph of $y=\sqrt{x}$ but is shifted down 3 units. $\mathrm{y}=\square$

1. The original function is $y = \sqrt{x}$ .
2. The transformation involves shifting the graph down by 3 units.

1. Understand the effect of shifting a graph vertically.
2. Apply the transformation to the original function.
3. Write the new function.

To shift the graph of $y = \sqrt{x}$ down by 3 units, we modify the function to $y = \sqrt{x} - 3$ .

The new function, after applying the vertical shift, is:
$y = \sqrt{x} - 3$
The function whose graph is the graph of $y = \sqrt{x}$ but shifted down 3 units is:
$\boxed{y = \sqrt{x} - 3}$