Question

Use the graph. What are the domain, period. range, and amplitude of the sine function? Where do the maximum and minimum values occur? Where do the zeros occur1. Domain 2. Period3. Range4. Amplitude5. Maximum Value at6. Minimum Value at7. Zeros (form least to greatest)

Answer 1

1. Domain

2. Period

3. Range

4. Amplitude

5. Maximum Value at

6. Minimum Value at

7. Zeros (form least to greatest)​

Part 1

Domain -----> data set of all possibles values of x

domain is the interval (-infinite, infinite) All real numbers

Part 2

Period

Remember that

For a trigonometric function, the length of one complete cycle is called a period

so

Period is the distance between pi/2 and 5pi/2

period=2pi

Part 3

Range ------> data set of all possible values of y

range is the interval {-1,1} All real numbers greater than or equal to -1 and less than or equal to 1

Part 4

Amplitude

Amplitude is the distance between the center line of the function and the top or bottom of the function

so

Amplitude=1

Part 5

Maximum Value at x=pi/2,5pi/2,9pi/2, 13pi/2 and x=-3pi/2,-7pi/2,-11pi/2

maximum value is y=1

Part 6

Minimum Value at x=3pi/2,7pi/2,11pi/2,.. and x=-pi/2,-5pi/2,-9pi/2,...

minimum value is y=-1

Part 7

Zeros (form least to greatest)​

-3pi,-2pi,-pi, 0,pi,2pi,3pi,..