Precalculus Trig Graphs Quiz – Free PDF

Contents

This precalculus trig graphs quiz asks 10 multiple-choice questions on graphs of trigonometric functions, and each answer comes with a short explanation.

Ten multiple-choice questions on amplitude, period, phase shift, range, tangent graphs, and models. Pick the one correct answer for each. Three questions include a graph.

PrecalculusCommon Core: F-TF.B.5 · F-IF.C.7e · F-BF.B.3

🎯 Graphs of Trigonometric Functions – Precalculus math quiz

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Question 1

What is the amplitude of \(y=-5\sin 3x+1\)?

A \(-5\)

B \(3\)

C \(5\)

D \(1\)

Question 2

What is the period of \(y=\cos\left(\frac{x}{4}\right)\)?

A \(\frac{\pi}{2}\)

B \(4\pi\)

C \(2\pi\)

D \(8\pi\)

Question 3

The graph is of a sine function. Which equation matches it?

Sine wave with a maximum (pi, 4) and a minimum (3pi, -2).

A \(y=3\sin 2x+1\)

B \(y=3\sin\left(\frac{x}{2}\right)+1\)

C \(y=4\sin\left(\frac{x}{2}\right)+1\)

D \(y=3\sin\left(\frac{x}{2}\right)-1\)

Question 4

What is the range of \(y=2\cos x-3\)?

A \(-5\le y\le -1\)

B \(-2\le y\le 2\)

C \(-6\le y\le 0\)

D \(-5\le y\le 1\)

Question 5

What is the phase shift of \(y=\cos(2x+\pi)\)?

A left \(\pi\)

B left \(\frac{\pi}{2}\)

C right \(\frac{\pi}{2}\)

D right \(\pi\)

Question 6

What is the period of the function graphed?

Tangent-shaped curve with asymptotes at x = -pi and x = pi.

A \(2\pi\)

B \(\pi\)

C \(\frac{\pi}{2}\)

D \(4\pi\)

Question 7

The graph shows a wave. Which function models it?

Wave with high points (0, 10), (12, 10) and low point (6, 4).

A \(h=3\cos\left(\frac{\pi t}{3}\right)+7\)

B \(h=3\cos\left(\frac{\pi t}{6}\right)+7\)

C \(h=7\cos\left(\frac{\pi t}{6}\right)+3\)

D \(h=3\sin\left(\frac{\pi t}{6}\right)+7\)

Question 8

What is the value of \(y=4\tan x\) at \(x=\frac{\pi}{4}\)?

A \(4\)

B \(1\)

C \(\pi\)

D \(\sqrt{2}\)

Question 9

Which describes the graph of \(y=\cos\left(x-\frac{\pi}{3}\right)+2\) compared with \(y=\cos x\)?

A left \(\frac{\pi}{3}\), up 2

B right \(\frac{\pi}{3}\), down 2

C right \(\frac{\pi}{3}\), up 2

D right 2, up \(\frac{\pi}{3}\)

Question 10

A periodic function has a maximum of 60 and a minimum of 20. What are its amplitude and midline?

A amplitude 40, midline \(y=20\)

B amplitude 20, midline \(y=20\)

C amplitude 40, midline \(y=40\)

D amplitude 20, midline \(y=40\)

🎉 Quiz complete!

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How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Amplitude is half the distance between the maximum and the minimum.
The period of sine and cosine is 2π divided by |B|; the period of tangent is π divided by |B|.
A positive C shifts the graph right; a positive D shifts it up.
Tangent has vertical asymptotes at x = π/2 + kπ and no amplitude.
A periodic data set with a known maximum and minimum fits a model with A = (M − m)/2 and D = (M + m)/2.