Question

In: Advanced Math

In this activity we have graphed the function y = sin(x). For this assignment, you will...

In this activity we have graphed the function y = sin(x). For this assignment, you will explore the changes that occur in the curve when we make simple changes to the function.

For each of the different parts below, create sketches and a description of the crucial properties of the periodic graphs including:

  • Period
  • Amplitude
  • Maximum
  • Minimum
  • Axis of the Curve
  • Zeros

Finally, in a few sentences, based on your findings describe how these changes in the function affect the properties of the curve.

Part A: Sketch a graph where the values of sin are multiplied by 2 (that is y = 2 sin(x)) and then sketch a graph where the values of sin are divided by 2 (that is y = ½ sin(x)).
Part B: Sketch a graph where the values of sin are have 1 added to them (that is y = sin(x) + 1) and then sketch a graph where the values of sin have 1 subtracted from them (that is y = sin(x) - 1).

For your sketches, you can scan hand-made sketches and email or fax these to your instructor. Alternately, you may use a simple drawing program like Windows Paint.

Solutions

Expert Solution

Part A

The graph of y=2 sin(x) is below

Period : ​​​​​​

Amplitude :2

Maximum : 2

Minimum : - 2

Axis of the curve : x-axis

Zero : ​​​​​​

The graph of y =(1/2) sin(x) is below

Period :​​​​​​

Amplitude : 0.5

Maximum : 0.5

Minimum : - 0.5

Axis of the curve :x-axis

Zero :​​​​​​

Part B

The graph of y =sin(x) +1 is below

Period :

Amplitude :1

Maximum :2

Minimum : 0

Axis of the curve : y=1

Zero :

The graph of y = sin (x) - 1 is below

Period :​​​​​​

Amplitude :1

Maximum: 0

Minimum : - 2

Axis of the curve : y=-1

Zero :

Colby Messinger answered 2 years ago
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