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| Both sides previous revision Previous revision Next revision | Previous revision | ||
| math:pre-ap_calculus [2025/05/14 16:41] – [Graphs of Functions] root1 | math:pre-ap_calculus [2025/05/14 16:47] (current) – [Transformations of Functions] root1 | ||
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| To graph \( y = cf(x) \), | To graph \( y = cf(x) \), | ||
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| If \( c > 1 \), stretch the graph of \( y = f(x) \) vertically by a factor of c. | If \( c > 1 \), stretch the graph of \( y = f(x) \) vertically by a factor of c. | ||
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| If \( 0 < c < 1 \), shrink the graph of \( y = f(x) \) vertically by a factor of c. | If \( 0 < c < 1 \), shrink the graph of \( y = f(x) \) vertically by a factor of c. | ||
| + | === Horizontal Stretching and Shrinking === | ||
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| + | To graph \( y = f(cx) \), | ||
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| + | If \( c > 1 \), stretch the graph of \( y = f(x) \) vertically by a factor of 1/c. | ||
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| + | If \( 0 < c < 1 \), shrink the graph of \( y = f(x) \) vertically by a factor of 1/c. | ||
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| + | === Even and Odd Functions === | ||
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| + | If a function \( f \) satisfies \( f(x) = f(-x) \) for every number \( x \) in its domain, then \( f \) is called an even function. | ||
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| + | If \( f \) satisfies \( f(x) = -f(-x) \) for every number \( x \) in its domain, then \( f \) is called an odd function. | ||
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| + | ==== Quadratic Functions; Maxima and Minima ==== | ||
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