How do you graph #-3 cos x#?

Answer 1
First graph #y=cos x#

graph{cos x [-10, 10, -5, 5]}

then apply the transformation by multiplying the #y# values by #-3#. This should vertically stretch the graph by a factor of #3#, and reflect the values across the #x# axis as well.

This should be the resulting graph:

graph{-3cos x [-10, 10, -5, 5]}

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Answer 2

To graph 3cos(x) -3 \cos(x) , you can start by understanding the graph of cos(x) \cos(x) . The cosine function oscillates between -1 and 1. Multiplying it by -3 simply flips the graph vertically and stretches it vertically by a factor of 3. So, the amplitude becomes 3, and the graph is inverted. The horizontal axis (x-axis) remains the same. This means the maximum value is -3 and the minimum value is 3. The graph will follow the same pattern as the cosine function, but with inverted peaks and troughs.

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Answer from HIX Tutor

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.

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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