If you graph a function and it looks like a circle, it will pass the vertical line test.

Mathematics

1 answer:

fgiga [73]3 years ago

4 0

Answer: false

Step-by-step explanation:

Since it is a circle, when you draw the line it will meet at two points which fails the vertical line test. In order to pass the vertical line test it must only meet at one point.

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Otrada [13]

Question:

1. vertical stretch of 2, horizontal stretch to a period of 2 pi, phase shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of 1 unit up

2. vertical compression of 2, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of 2 units down

3. vertical compression of 2, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of 1 unit down

4. vertical stretch of 2, horizontal compression to a period of StartFraction pi Over 2 EndFraction, phase shift of Pi units to the right, vertical shift of 1 unit down

Answer:

The correct option is;

4. Vertical stretch of 2, horizontal compression to a period of π/2, phase shift of π units to the right, vertical shift of 1 unit down

Step-by-step explanation:

Here, we have the parent cosine function given by y = cos(x)

A plot of the above function is attached

By comparison, it is observed that the transformation required to change the parent function includes;

1. Vertical stretch from the parent function of amplitude 1 to amplitude 2

2. A horizontal compression so that the period of one complete revolution is π/2 rather than 2·π in the parent cosine function

3. Phase shift of pi units to the right such that cos(π) = 1 rather than cos(2π) = 1 as it applies to the parent function

4. Shift of the y values from the symmetrical x-axis origin downwards by 1 unit such that the maximum y value of the doubly stretched transformation is 1 rather than 2