A Guide on Transformations of Functions
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2022/2023
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A Guide on Transformations of Functions
A Guide on Transformations of Functions VERTICAL SHIFTS OF GRAPHS. ya gi) +3 Suppose ¢ > O. - To graph y — f(x) 1c, shift the graph of y — f(x) upward c units fw — 2 To graph y — f(x) = 6, shilL the graph of y ~ f(x) downward ¢ units Aix) — x*-2 Pee HORIZONTAL SHIFTS OF GRAPHS Suppose ¢ > 0. , ay , in, ax) = (x44) f(x) — x? A(x) = (x-2/? lo graph y — f(x — ©), shift the graph of y — f(x) to the right ¢ units, To graph y = f(x |e), shift the gruph of y = f(x) Ww the left ¢ units, y field REFLECTING GRAPHS To graph y — —J(x), reflect the graph of y — f(x) in the x-axis, To graph y = f(x), reflect the graph of y = f(x) in the y-axis. ya y= Sa) 0 s yo—fia) VERTICAL STRETCHING AND SHRINKING OF GRAPHS To graph y = cf(x): Ife > 1, stretch the graph of y — /(x) vertically by a factor of c. Ifo