Vertical Stretch and Shrink of a Function

The graph of a function can be vertically stretched or shrunk by multiplying the function rule by a positive number

a .

y = a \cdot f (x)

The vertical distance between the graph and the

x -

axis will then change by the factor

a

at every point on the graph. If

a > 1,

this will lead to the graph being stretched vertically. Similarly,

a < 1

leads to the graph being shrunk vertically. Note that

x -

intercepts have the function value

0 .

Therefore, they are not affected by this transformation.

The general form of this transformation is shown in the table.

Transformations of $f (x)$
Vertical Stretch or Shrink	Vertical stretch, $a > 1$ $y = a f (x)$
Vertical Stretch or Shrink	Vertical shrink, $0 < a < 1$ $y = a f (x)$

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