# How do you use the amplitude and period to graph #y= 2 sin (-2x+pi) +1#?

As detailed below.

Given equation is y = 2 sin (-2x + pi) + 1#

graph{-2sin(2x-pi) + 1 [-10.125, 9.875, -4.84, 5.16]}

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To graph the function (y = 2 \sin(-2x + \pi) + 1), first, identify the amplitude and period.

The amplitude of a sine function is the distance between the maximum and minimum values of the function, which is the absolute value of the coefficient of sine. In this case, the amplitude is 2.

The period of a sine function is the distance between two consecutive peaks (or troughs) of the graph. It is calculated using the formula (T = \frac{2\pi}{|b|}), where (b) is the coefficient of (x). In this case, (b = -2), so the period is (T = \frac{2\pi}{|-2|} = \pi).

Now, to graph the function, start by marking the key points. Since the coefficient of (x) is negative, the graph of the function will be reflected about the y-axis.

- Mark the vertical shift, which is 1 unit upward from the x-axis.
- Since the amplitude is 2, the maximum and minimum values will be 2 units above and below the midline, respectively.
- The period is (\pi), so the distance between two consecutive peaks (or troughs) is (\pi) units.
- Plot additional points using the period and amplitude. Remember that the sine function starts at the midline, then goes up to its maximum, returns to the midline, goes down to its minimum, and returns to the midline in one period.

With these key points marked, draw the graph by connecting them smoothly. Ensure that the graph reflects the effect of the negative coefficient of (x) by noting the direction of the sine curve.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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