1.3 New Functions from Old

1.3 New Functions from Old - Yc=f(x c> 1 vertical...

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New Functions from Old Translations: Y=f(x): Y=f(x-a) – Shifts right a units Y-b=f(x) – shifts up b units Y-b=f(x-a) – shifts up b units and right a units Reflections: Y=f(x): -Y=f(x) – Reflects about the x-axis Y=f(-x) – Reflects about the y-axis Stretching/Compressing: Y=f(x): Y=f(cx) c > 1 horizontal compression Y=f(cx) c < 1 horizontal stretch
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Unformatted text preview: Yc=f(x) c > 1 vertical compression Yc=f(x) c < 1 vertical stretch Composition: Y=f(x): FoG(x) = f[g(x)] usually these two are not the same, Y=g(x): GoF(x) = g[f(x)] unless they are inverses ex: f(x) = cos x g(x) = 3x^2+2 FoG(x)= cos[g(x)] = cos (3x^2+2) GoF(x) = 3[f(x)]^2+2 = 3cos^2x+2...
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