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Worked solution

Sketch the reciprocal of a shifted line

Given f(x)=x+4f(x)=x+4, sketch y=1/f(x)y=1/f(x).

CJC · Transformations · Self-Practice 7

Sketch both reciprocal branches

Answer

y=1/(x+4)y=1/(x+4), asymptotes x=−4x=-4, y=0y=0, y-intercept (0,1/4)(0,1/4).

Independently derived: the original zero at x=−4x=-4 is excluded and becomes a vertical asymptote. Outputs are negative for x<−4x<-4 and positive for x>−4x>-4; neither branch crosses the x-axis. Neither copy prints a self-practice solution on this page.

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Independent sketch of 1/(x+4), with vertical asymptote −4, horizontal 0, y-intercept 1/4, negative left branch and positive right branch.
Independent sketch of 1/(x+4), with vertical asymptote −4, horizontal 0, y-intercept 1/4, negative left branch and positive right branch.
Independent sketch of 1/(x+4), with vertical asymptote −4, horizontal 0, y-intercept 1/4, negative left branch and positive right branch.
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