Porisma

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Map labelled points and preserve reciprocal domains

The given graph is y=f(x)y=f(x), with maximum A=(2,2), B=(4,0), C=(0,1) and vertical asymptote x=5; its left tail approaches y=0. Sketch on separate diagrams:

(i) y=f(2x−1)y=f(2x-1); marks

(ii) y=f(x/2)−2y=f(x/2)-2; marks

(iii) y=1/f(x)y=1/f(x); marks

Show the corresponding A,B,C coordinates and all asymptotes where applicable.

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Source schematic y=f(x), A(2,2) maximum,C(0,1),B(4,0), vertical asymptote x=5 and left tail tending to y=0. Only the supplied branch x<5 is reconstructed. Interpolation is qualitative.
Source schematic y=f(x), A(2,2) maximum,C(0,1),B(4,0), vertical asymptote x=5 and left tail tending to y=0. Only the supplied branch x<5 is reconstructed. Interpolation is qualitative.
Source schematic y=f(x), A(2,2) maximum,C(0,1),B(4,0), vertical asymptote x=5 and left tail tending to y=0. Only the supplied branch x<5 is reconstructed. Interpolation is qualitative.

CJC · Review problems · Question 2

A reciprocal has the same input domain, further excluding zeros of f.

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