Quick questions on Combining functions: sums, differences, products, quotients, squares and reciprocals

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is build the reciprocal graph, stage by stage?

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The reciprocal

y = \frac{1}{f}

is the most-examined combination, and the safest way to sketch it is to mark the structure from

f

first, then draw. Below,

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

is built from

f(x) = x^2 - 1

one decision at a time. (The 2022 HSC asked exactly this kind of "describe the features of

\frac{1}{f}

" question.)

What are square has zeros, not just minimums?

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f^2

has zeros wherever

f

does. The graph touches the

x

-axis at each one rather than crossing.

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