Before Quiz 2

Judging a symmetry from the look of the formula

The habit: Test the definition instead: substitute −x and compare the result with f(x) and −f(x), and accept a period only when every term repeats after it.

3 practice questions are built to catch it, in 2 topics.

Practise against it: 2 questions

What it looks like

A question from curve sketching, with the answer this slip gives beside the right one.

Introductory1 mark · 2 min

Which of the following functions is even?

With the slip: $\displaystyle x^{4} + 5x^{2} + \sin\!\left(x^{3}\right)$
Worked through: $\displaystyle x^{4} + 5x^{2} + \cos\!\left(x^{3}\right)$

Even powers alone do not make the sum even: sin(x³) is odd, since sin(−x³) = −sin(x³). At x = ±1 the values are 6 + sin 1 and 6 − sin 1.

See the worked solution

Where it comes up

Power functions and first sketches1 question
Curve sketching2 questions

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

01
The graph of one of these power functions is shown, with the points $(-1, -1)$ and $(1, 1)$ marked. Which function is it?
Power functions and first sketchesIntroductory
02
A function $f$ is even, and its graph for $x \geq 0$ is shown. Counting both sides of the $y$ -axis, how many local extrema (local maxima and local minima together) does $f$ have?
Curve sketchingChallenging

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