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Chapter 1 | Functions and Graphs
Figure 1.24 (a) For c >0, the graph of y = f ( x + c ) is a horizontal shift left c units of the graph of y = f ( x ). (b) For c >0, the graph of y = f ( x − c ) is a horizontal shift right c units of the graph of y = f ( x ).
A vertical scaling of a graph occurs if we multiply all outputs y of a function by the same positive constant. For c >0, the graph of the function cf ( x ) is the graph of f ( x ) scaled vertically by a factor of c . If c >1, the values of the outputs for the function cf ( x ) are larger than the values of the outputs for the function f ( x ); therefore, the graph has been stretched vertically. If 0< c <1, then the outputs of the function cf ( x ) are smaller, so the graph has been compressed. For example, the graph of the function f ( x ) =3 x 2 is the graph of y = x 2 stretched vertically by a factor of 3, whereas the graph of f ( x ) = x 2 /3 is the graph of y = x 2 compressed vertically by a factor of 3 ( Figure 1.25 ).
Figure 1.25 (a) If c >1, the graph of y = cf ( x ) is a vertical stretch of the graph of y = f ( x ). (b) If 0< c <1, the graph of y = cf ( x ) is a vertical compression of the graph of y = f ( x ).
The horizontal scaling of a function occurs if we multiply the inputs x by the same positive constant. For c >0, the graph of the function f ( cx ) is the graph of f ( x ) scaled horizontally by a factor of c . If c >1, the graph of f ( cx ) is the graphof f ( x ) compressed horizontally. If 0< c <1, the graph of f ( cx ) is the graph of f ( x ) stretched horizontally. For
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