Question

The height of a saw tooth in inches after time in seconds is represented by the function y = 0.3sin (30x + 1.5) - 0.1 for t > 0. Without graphing the function, determine the range that the saw tooth covers.

Answer 1

Answer:

Range is from -0.4 till 0.2, inclusive

Step-by-step explanation:

y = 0.3sin (30x + 1.5) - 0.1

-1 < sin(x) < 1

-1 < sin(30x + 1.5) < 1

Because this is a change in domain, not in range

-0.3 < 0.3sin(30x + 1.5) < 0.3

-0.3-0.1 < 0.3sin(30x + 1.5) - 0.1 < 0.3-0.1

-0.4 < 0.3sin(30x + 1.5) - 0.1 < 0.2

Answer 2

The sin function wiggles between  -1  and  +1 .

When the sin is  -1,  y = -0.3 - 0.1  =  -0.4

When the sin is  +1, y = +0.3 - 0.1  =  +0.2

So the total range of  'y'  is        -0.4 < y < +0.2 .