Question 1

What is the effect of the transformation

y = \sin(x + \frac{\pi}{2})

on the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the left.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units down.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the right.

Answer

The graph is reflected over the x-axis.

Question 2

How does the graph of

y = \sin(x + \frac{\pi}{2})

compare to the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts 3 units upwards.

Answer

The graph shifts 3 units downwards.

Answer

The graph shifts 3 units to the right.

Answer

The graph stretches vertically by a factor of 3.

Question 3

What is the result of applying the transformation

y = \sin(x + \frac{\pi}{2})

to the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the right.

Answer

The graph is compressed horizontally by a factor of

y = \sin(x + \frac{\pi}{2})

.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the left.

Answer

The graph is stretched vertically by a factor of

y = \sin(x + \frac{\pi}{2})

.

Question 4

If the graph of

y = \sin(x + \frac{\pi}{2})

is transformed to

y = \sin(x)

, what change occurs?

Accepted Answer

The graph is compressed horizontally by a factor of 2.

Answer

The graph shifts vertically by 2 units.

Answer

The graph is stretched horizontally by a factor of 2.

Answer

The amplitude of the graph doubles.

Question 5

How does the graph of

y = \sin(x + \frac{\pi}{2})

differ from the graph of

y = \sin(x)

?

Accepted Answer

The graph is reflected over the x-axis.

Answer

The graph shifts vertically by 2 units.

Answer

The graph is stretched vertically by a factor of 2.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the right.

Question 6

What does the transformation

y = \sin(x + \frac{\pi}{2})

do to the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the right.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units upward.

Answer

The graph is stretched vertically.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the left.

Question 7

What effect does the transformation

y = \sin(x + \frac{\pi}{2})

have on the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts 2 units downward.

Answer

The graph is reflected over the x-axis.

Answer

The graph stretches horizontally by a factor of 2.

Answer

The graph shifts 2 units upward.

Question 8

How does the graph of

y = \sin(x + \frac{\pi}{2})

compare to the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the left.

Answer

The period of the graph doubles.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units to the right.

Answer

The graph shifts

y = \sin(x + \frac{\pi}{2})

units upward.

Question 9

What is the effect of the transformation

y = \sin(x + \frac{\pi}{2})

on the graph of

y = \sin(x)

?

Accepted Answer

The graph's amplitude is doubled.

Answer

The graph is reflected over the x-axis.

Answer

The graph shifts 2 units to the right.

Answer

The period of the graph doubles.

Question 10

What transformation does

y = \sin(x + \frac{\pi}{2})

apply to the graph of

y = \sin(x)

?

Accepted Answer

The graph shifts 1 unit downward.

Answer

The graph shifts 1 unit to the left.

Answer

The graph is reflected over the y-axis.

Answer

The graph shifts 1 unit upward.

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