TRANSFORMATIONS OF FUNCTIONS WORKSHEET

Problem 1 :

Do the following transformation to the function y = √x.

'A translation to the right by 3 units'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Problem 2 :

Do the following transformation to the function y = √x.

'A translation upward by 3 units'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Problem 3 :

Do the following transformation to the function y = √x.

'A reflection through the x-axis'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Problem 4 :

Do the following transformation to the function y = √x.

'A reflection through the y-axis'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Problem 5 :

Do the following transformation to the function y = √x.

'A horizontal expansion by a factor 0.5'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Problem 6 :

Do the following transformation to the function y = √x.

'A vertical expansion by a factor 0.5'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answers

Problem 1 :

Do the following transformation to the function y = √x.

'A translation to the right by 3 units'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answer :

Step 1 :

Since we do a translation to the right by 3 units, we have to replace x by x - 3 in the given function

y = √x

Step 2 :

So, the formula that gives the requested transformation is

y = √(x - 3)

Step 3 :

The graph y = √(x - 3) can be obtained by translating the graph of y = √x to the right by 3 units.

Step 4 :

The graph of the original function (given function).

Step 5 :

The graph of the transformed function.

Problem 2 :

Do the following transformation to the function y = √x.

'A translation upward by 3 units'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answer :

Step 1 :

Because we do a translation towards upward by 3 units, we have to replace y by y - 3 in the given function

y = √x 

Step 2 :

So, the formula that gives the requested transformation is

y - 3 = √x

or

y = √x + 3

Step 3 :

The graph y = √x + 3 can be obtained by translating the graph of y = √x  toward upward by 3 units.

Step 4 :

The graph of the original function (given function).

Step 4 :

The graph of the transformed function.

Problem 3 :

Do the following transformation to the function y = √x.

'A reflection through the x-axis'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answer :

Step 1 :

Since we do reflection transformation through the x-axis, we have to replace y by -y in the given function y = √x.

Step 2 :

So, the formula that gives the requested transformation is

-y = √x

Multiply each side by negative sign. 

y = -√x 

Step 3 :

The graph y = -√x  can be obtained by reflecting the graph of y = -√x through the x-axis  using the rule given below. 

(x, y) ----> (x , -y)

Step 4 :

The graph of the original function (given function)

Step 5 :

The graph of the transformed function.

Problem 4 :

Do the following transformation to the function y = √x.

'A reflection through the y-axis'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answer :

Step 1 :

Since we do reflection transformation through the y-axis, we have to replace x by -x in the given function

y = √x 

Step 2 :

So, the formula that gives the requested transformation is

y = √-x 

Step 3 :

The graph y = √-x  can be obtained by reflecting the graph of y = √x through the y-axis  using the rule given below.

(x, y) ----> (-x , y)

Step 4 :

The graph of the original function (given function)

Step 5 :

The graph of the transformed function.

Problem 5 :

Do the following transformation to the function y = √x.

'A horizontal expansion by a factor 0.5'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answer :

Step 1 :

Since we do horizontal expansion by the factor 0.5, we have to replace x by 0.5x in the given function y = √x.

Step 2 :

So, the formula that gives the requested transformation is

y = √0.5x 

Step 3 :

The graph y = √0.5x can be obtained by expanding the graph of the function y = √x horizontally by the factor 0.5.

(x, y) ----> (0.5x, y)

Step 4 :

The graph of the original function (given function)

Step 5 :

The graph of the function in which horizontal expansion made by the factor 0.5.

Problem 6 :

Do the following transformation to the function y = √x.

'A vertical expansion by a factor 0.5'

And also write the formula that gives the requested transformation and draw the graph of both the given function and the transformed function.

Answer :

Step 1 :

Since we do vertical expansion by the factor 0.5, we have to replace y by 0.5y in the given function y = √x.

Step 2 :

So, the formula that gives the requested transformation is

0.5y = √x

or

y = 2√x  

Step 3 :

The graph y = 2√x can be obtained by expanding the graph of the function y = √x vertically by the factor 0.5. 

(x, y) -----> (x, 0.5y)

Step 4 :

The graph of the original function (given function).

Step 5 :

The graph of the function in which vertical expansion made by the factor 0.5.

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