HORIZONTAL STRETCH AND COMPRESSION

Example 1 :

Perform a horizontal stretch by a factor 2 to the function

f(x) = (x - 1)²

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 :

Let g(x) be a function which represents f(x) after the horizontal stretch by a factor of 2.

Since we do horizontal stretch by the factor 2, we have to replace x by (1/2)x in f(x) to get g(x).

Step 2 :

So, the formula that gives the requested transformation is

g(x) = f[(1/2)x]

g(x) = [(1/2)x - 1]²

Step 3 :

The graph g(x) = [(1/2)x - 1]² can be obtained by stretching the graph of the function f(x) = (x - 1)² vertically by the factor 2.

(x, y) -----> (2x, y)

Step 4 :

Table of values :

Step 5 :

Graphs of f(x) and g(x) :

Example 2 :

Perform an horizontal compression by a factor 2 to the function

f(x) = (x - 1)²

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 :

Let g(x) be a function which represents f(x) after the vertical compression by a factor of 2.

Since we do vertical compression by the factor 2, we have to replace x by 2x in f(x) to get g(x).

Step 2 :

So, the formula that gives the requested transformation is

g(x) = f(2x)

g(x) = (2x - 1)²

Step 3 :

The graph g(x) = (2x - 1)² can be obtained by compressing the graph of the function f(x) = (x - 1)² vertically by the factor 2.

(x, y) -----> ((1/2)x, y)

Step 4 :

Table of values :

Step 5 :

Graphs of f(x) and g(x) :

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