Porisma

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Compare modulus, negative scaling and reciprocal graphs

The given graph y=f(x)y=f(x) has asymptotes x=−1x=-1, y=−2y=-2, turning point A=(1,3)A=(1,3), and zeros O=(0,0)O=(0,0), B=(−2,0)B=(-2,0), C=(4,0)C=(4,0).

(a) State the turning point of y=1+13f(x)y=1+\frac13f(x). mark

(b) Sketch y=∣f(x)∣y=|f(x)|, labelling asymptotes and the points corresponding to A,B,C. marks

(c) Sketch y=−f(2x)y=-f(2x) with those labels. marks

(d) Sketch y=1/f(x)y=1/f(x), labelling asymptotes, turning points and axis crossings. marks

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Qualitative reconstruction checked against the actual given graph in lecture Student PDF 38 / printed 110 and Teacher PDF 39 / printed 111: A(1,3), B(−2,0), O(0,0), C(4,0), asymptotes x=−1,y=−2, with the source branch directions. The standalone solution PDF omits that original figure; no unique formula is inferred.
Qualitative reconstruction checked against the actual given graph in lecture Student PDF 38 / printed 110 and Teacher PDF 39 / printed 111: A(1,3), B(−2,0), O(0,0), C(4,0), asymptotes x=−1,y=−2, with the source branch directions. The standalone solution PDF omits that original figure; no unique formula is inferred.
Qualitative reconstruction checked against the actual given graph in lecture Student PDF 38 / printed 110 and Teacher PDF 39 / printed 111: A(1,3), B(−2,0), O(0,0), C(4,0), asymptotes x=−1,y=−2, with the source branch directions. The standalone solution PDF omits that original figure; no unique formula is inferred.

[2022/YIJC/Promo/6]

CJC · Review problems · Question 5

Distinguish |f(x)|,−f(2x), and 1/f(x): each changes points in a different way.

Read the worked solution