Porisma

Worked solution

Keep the order of horizontal translation and scaling

Explain how the graph of y=2/(3x−1)y=2/(3x-1) may be obtained from y=1/xy=1/x by appropriate transformations.

CJC · Discussion · Question 1

Answer

Translate right 1, scale parallel to x by 1/3, then scale parallel to y by 2.

Translate one unit right

y=1/x⟶y=1/(x−1)y=1/x\longrightarrow y=1/(x-1).

How did this part go?

Scale parallel to x by 1/3

Replacing x by 3x gives y=1/(3x−1)y=1/(3x-1). The preceding translated position is scaled as well; its pole moves from x=1 to x=1/3.

How did this part go?

Scale parallel to y by 2

y/2=1/(3x−1)y/2=1/(3x-1), hence y=2/(3x−1)y=2/(3x-1). The ordered source sequence is right 1, horizontal scale 1/3, vertical scale 2.

How did this part go?

Common mistakes

A translation followed by horizontal scaling does not equal the same operations in reversed order.

Solution notes

All printed equations and the exact ordered sequence retained. This Discussion sheet prints no mark allocations for these questions; none invented.

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