Choose the function matching the displayed graph.

01 / Standard#Your turn

Official paper · jm01-2021 · I.11 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Read the maximum and minimum to find the midline and amplitude.

Hint 2

Measure the distance between consecutive peaks.

Worked solution

The graph ranges from 1 to 5, so its midline is 3 and amplitude is 2.
$c=(5+1)/2=3,\quad A=(5-1)/2=2$
Peaks at zero and π give period π and frequency 2.
$T=\pi\Rightarrow\omega=2\pi/T=2$
The graph begins at a maximum, agreeing with positive cosine.
$y=3+2\cos2x$

B: y=3+2cos 2x.

Checks and common pitfalls: Frequency is obtained from a full cycle, not the peak-to-trough half-cycle.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
The graph ranges from 1 to 5, so its midline is 3 and amplitude is 2.
$c=(5+1)/2=3,\quad A=(5-1)/2=2$
Peaks at zero and π give period π and frequency 2.
$T=\pi\Rightarrow\omega=2\pi/T=2$
The graph begins at a maximum, agreeing with positive cosine.
$y=3+2\cos2x$

Think first. Reveal a hint when the class is ready.

2021 JM01