Sketch reciprocal-function pairs and describe their features.

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Sketch reciprocal-function pairs and describe their features. (1) Sketch each pair of functions on the same set of axes. Include all axes intercepts and asymptotes. i.

y=x^2

and

y=\frac{1}{x^2}

ii.

y=-(x-1)^2

and

y=-\frac{1}{(x-1)^2}

iii.

y=x^2+4

and

y=\frac{1}{x^2+4}

iv.

y=-(x^2-4)

and

y=-\frac{1}{x^2-4}

y=(x-1)(x-3)

and

y=\frac{1}{(x-1)(x-3)}

(2) How can the vertical asymptotes of

y=\frac{1}{f(x)}

be established from

f(x)

without first viewing its graph? (3) What other observations can you make about the graph of

y=\frac{1}{f(x)}

Related theory

Rational Functions
Functions

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