# How do you graph #f(x)= 2 sin 4x#?

So the graph becomes :

graph{2sin(4x) [-4.385, 4.384, -2.19, 2.195]}

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To graph ( f(x) = 2 \sin(4x) ), follow these steps:

- Start with the sine function ( y = \sin(x) ) as your base function.
- Apply the vertical stretch by a factor of 2 to the sine function, which means multiplying the y-values by 2.
- Apply the horizontal compression by a factor of (\frac{1}{4}), which means dividing the x-values by 4.
- Plot points on the graph by choosing values of ( x ), calculating ( f(x) ), and then plotting the corresponding points.
- Connect the points smoothly to form the graph.

Remember that the period of ( \sin(4x) ) is ( \frac{2\pi}{4} = \frac{\pi}{2} ), which means the graph repeats every ( \frac{\pi}{2} ) units.

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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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