QuestionWhich function's graph is $y=\frac{1}{x}$ shifted right 5 units and up 2 units? $y=\frac{1}{x+5}+2$

Studdy Solution

STEP 1

Assumptions1. The original function is $y=\frac{1}{x}$ . The function is shifted to the right by5 units3. The function is shifted up by units

STEP 2

The general form of a function after a horizontal and vertical shift is given by $y=f(x-h)+k$ , where $h$ is the horizontal shift and $k$ is the vertical shift.

STEP 3

For a shift to the right, $h$ is subtracted from $x$ . For a shift up, $k$ is added to the function.

STEP 4

Substitute the given shifts into the general form of the function. Here, $h=$ and $k=2$ .
$y=\frac{1}{x-}+2$

STEP 5

So, the function that is the same as the graph of $y=\frac{1}{x}$ shifted to the right5 units and shifted up2 units is $y=\frac{1}{x-5}+2$ .

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QuestionWhich function's graph is $y=\frac{1}{x}$ shifted right 5 units and up 2 units? $y=\frac{1}{x+5}+2$

Studdy Solution

STEP 1

Assumptions1. The original function is $y=\frac{1}{x}$ . The function is shifted to the right by5 units3. The function is shifted up by units

STEP 2

The general form of a function after a horizontal and vertical shift is given by $y=f(x-h)+k$ , where $h$ is the horizontal shift and $k$ is the vertical shift.

STEP 3

For a shift to the right, $h$ is subtracted from $x$ . For a shift up, $k$ is added to the function.

STEP 4

Substitute the given shifts into the general form of the function. Here, $h=$ and $k=2$ .
$y=\frac{1}{x-}+2$

STEP 5

So, the function that is the same as the graph of $y=\frac{1}{x}$ shifted to the right5 units and shifted up2 units is $y=\frac{1}{x-5}+2$ .

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QuestionWhich function's graph is y=1xy=\frac{1}{x}y=x1​ shifted right 5 units and up 2 units? y=1x+5+2y=\frac{1}{x+5}+2y=x+51​+2

Studdy Solution

STEP 1

Assumptions1. The original function is y=1xy=\frac{1}{x}y=x1​ . The function is shifted to the right by5 units3. The function is shifted up by units

STEP 2

The general form of a function after a horizontal and vertical shift is given by y=f(x−h)+ky=f(x-h)+ky=f(x−h)+k, where hhh is the horizontal shift and kkk is the vertical shift.

STEP 3

For a shift to the right, hhh is subtracted from xxx. For a shift up, kkk is added to the function.

STEP 4

Substitute the given shifts into the general form of the function. Here, h=h=h= and k=2k=2k=2.y=1x−+2y=\frac{1}{x-}+2y=x−1​+2

STEP 5

So, the function that is the same as the graph of y=1xy=\frac{1}{x}y=x1​ shifted to the right5 units and shifted up2 units is y=1x−5+2y=\frac{1}{x-5}+2y=x−51​+2.

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QuestionWhich function's graph is $y=\frac{1}{x}$ shifted right 5 units and up 2 units? $y=\frac{1}{x+5}+2$

Assumptions1. The original function is $y=\frac{1}{x}$ . The function is shifted to the right by5 units3. The function is shifted up by units

The general form of a function after a horizontal and vertical shift is given by $y=f(x-h)+k$ , where $h$ is the horizontal shift and $k$ is the vertical shift.

For a shift to the right, $h$ is subtracted from $x$ . For a shift up, $k$ is added to the function.

Substitute the given shifts into the general form of the function. Here, $h=$ and $k=2$ .
$y=\frac{1}{x-}+2$

So, the function that is the same as the graph of $y=\frac{1}{x}$ shifted to the right5 units and shifted up2 units is $y=\frac{1}{x-5}+2$ .