If a sine curve has a vertical shift down 19 units with an amplitude of 21, what will the minimum and maximum values be? (i. e. how high and low will the graph go?) Min Value:
Max Value:

Given:

Amplitude = 21

Vertical shift = 19 units down

To find:

The maximum and the minimum value.

Solution:

The general form of sine function is:

Where, |A| is amplitude, is period, is phase shift and D is the vertical shift.

Here,

We have,

Amplitude:

Vertical shift:

Negative sign means shifts downwards.

Now,

And,

Therefore, the minimum value is -40 and the maximum value is 2.

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: