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29) y=f(x+3)-230) y=-2f(x)31) y-f(2x)

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29) y=f(x+3)-2
30) y=-2f(x)
31) y-f(2x)
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29) y=f(x+3)-2 30) y=-2f(x) 31) y-f(2x)

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Step 1

From the given diagram the points of the graph of y= f(x) are (–1,–2),(0,1) and (2,–1).

 

Given function is y= f(2x).

 

Note that, f(kx) stretches/ shrinks f(x) horizontally. That is, y=f(kx) is the graph of f(x) horizontally shrunk or compressed by dividing each of it’s x - coordinates by k.

 

Step 2

For transformation of graph of the function y=f(x) to y= f(2x) divide each of x - coordinates by 2.

 

Then the coordinates of the graph of the function y= f(2x) are (–0.5,–2), (0,1) and (1,–1).

 

Step 3

Plot these points and connect them with a smooth curve.

 

The graph of the funct...

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Algebra

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