0. Functions

In Exercises 59–62, sketch the graph of the given function. What is the period of the function?

𝔂 = cos πx/2

Graph the functions in Exercises 13–22. What is the period of each function?

sin (x/2)

Graph the functions in Exercises 13–22. What is the period of each function?

−cos 2πx

Graph the functions in Exercises 13–22. What is the period of each function?

sin (x − π/4) + 1

Graph the functions in Exercises 23–26 in the ts-plane (t-axis horizontal, s-axis vertical). What is the period of each function? What symmetries do the graphs have?

s = −tan πt

[Technology Exercise]

a. Graph y = cos x and y = sec x together for −3π/2 ≤ x ≤ 3π/2. Comment on the behavior of sec x in relation to the signs and values of cos x.

Graph y = sin x and y = ⌊sin x⌋ together. What are the domain and range of ⌊sin x⌋?

Finding a Viewing Window

In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.

y = 3 cos 60x

Finding a Viewing Window

In Exercises 5–30, find an appropriate graphing software viewing window for the given function and use it to display that function’s graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function.

y = x + (1/10) sin 30x

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph four periods of the function f (x) = −tan 2x.

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph two periods of the function f (x) = 3 cot (x/2) + 1.

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the function f (x) = sin 2x + cos 3x.

Use graphing software to graph the functions specified in Exercises 31–36.

Select a viewing window that reveals the key features of the function.

Graph the function f (x) = sin³ x.

General Sine Curves

For

f(x) = A sin ((2π/B)(x – C) +D

identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.

y = ½ sin (πx – x) + ½

General Sine Curves

For

f(x) = A sin ((2π/B)(x – C) +D

identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.

y = L/2π sin (2πt/L), L > 0