Before the midterm

Shifting the graph the wrong way

The habit: Inside the function the sign is reversed: x minus 3 moves the graph right, x plus 3 moves it left.

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

See it fail in a figure: The wrong way, in the functions, graphs and inverses lesson

What it looks like

A question from power functions and first sketches, with the answer this slip gives beside the right one.

Standard2 marks · 4 min

A person’s core body temperature, in degrees Celsius, is modelled by the function below, where $t$ is the time in hours after midnight. At what time $t$ , with $0 \leq t < 24$ , is the temperature highest?

T(t) = 36.9 + 0.4\sin\!\left(\frac{\pi}{12}(t - 11)\right)

With the slip: $\displaystyle 19$
Worked through: $\displaystyle t = 17 \ \text{(5 p.m.)}$

19 is −5 + 24: the peak of sin(πt/12) at t = 6 moved 11 hours earlier, then brought back into the day. t − 11 delays the cycle, so the peak moves 11 hours later instead.

See the worked solution

Where it comes up

Power functions and first sketches1 question
Functions, graphs and inverses1 question
Functions of two variables and partial derivatives1 question

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 $y = f(x)$ is shifted 3 units to the right and then reflected in the $x$ -axis. Which formula describes the resulting graph?
Functions, graphs and inversesIntroductory
02
Let $f(x, y) = x^{2} - 4x + y^{2}$ . Which describes the level curve $f(x, y) = 5$ ?
Functions of two variables and partial derivativesIntroductory

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