Algebra II - Graphs and Amplitude

domain

the set of first coordinates in a relation; the set of independent variable (x) values

The graph shows a trigonometric function. The period of the function is _________, the amplitude of the function is ____________and the midline of the function is y = _______.

2, 2, 3

The amplitude of y = -3sinx is _____.

3

The range of y = 2 / 3 sin x for π ≤ x ≤ is _____.

- 2 / 3 ≤ y ≤ 0

Which of the following functions corresponds to the sinusoid shown above?

-4 cos 3x

Which of the following functions has an amplitude of 5 and passes through the point (0,0)?

-5 sin x

Use complete sentences to describe the domain of the cosine function.

The domain for the cosine function is all real numbers. It is periodic and it will repeat the pattern over intervals of 2 pi. ( Actually idk if I'm wrong here or not, I'll likely edit this later because for me I feel that the thought of my answer is just incomplete. Sorry abt that )

periodic function

a function that repeats a pattern over its domain

asymptotes

lines that a graph approaches but never touches

The range of F(x) = 5cosx is _____.

-5 ≤ F(x) ≤ 5

What is the frequency of the function y = cos5x?

5

The period of y = sin x / 4 is _____.

8 π

period of a function

the displacement of x at which the graph of a function begins to repeat

amplitude

the maximum displacement from the horizontal line of symmetry for the sine and cosine functions

frequency

the number of times the pattern in the graph repeats within 2 π for the sine, cosine, and their reciprocal functions, or within π for the tangent and cotangent functions; in physics, the number of waves (vibrations, revolutions, or cycles) that pass a given point per unit of time

range

the set of second coordinates in a relation; the set of dependent variable (y) values

What is the correct equation for the function whose graph is shown?

y = -2 sin 6 x

Choose the equation of the graph shown. ( I can't upload photos, but to give you an idea of the graph, it passes through 0 and pi of the x-axis, with a maximum of 2 and a minimum of -2 )

y = -2sin x

Choose the correct equation for the function whose graph is shown.

y = 3 / 2 sin4 x

Which of the following cosine functions has a period of 3π?

y = cos 2 / 3 x