Question 1

Which transformation is applied to the function $$f(x) = \sin(x) to $$obtain the graph shown in the second image, where the maximum is at $$\left(\frac{\pi}{2}, 1\right)$$ and the minimum is at $$\left(\frac{3\pi}{2}, -1\right)$$?

Accepted Answer

No transformation; this is the basic graph of $$f(x) = \sin(x)$$

Question 2

If the function $$f(x) = \sin(x) is $$transformed to $$g(x) = \sin(x - \pi)$$, what happens to the graph?

Accepted Answer

It is shifted horizontally right $$\pi$$ units

Question 3

Given $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = -\sin(x)$$?

Accepted Answer

Reflection about the x-axis

Question 4

If $$f(x) = \sin(x)$$, what is the domain and range of $$f(x) as $$shown in the second image?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$[-1, 1]$$

Question 5

What transformation would result in the graph $$g(x) = \sin(x) + 2$$?

Accepted Answer

Vertical shift up 2 units

Question 6

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = \sin(2x)$$?

Accepted Answer

Horizontal compression by a factor of $$\frac{1}{2}$$

Question 7

Which transformation would produce the graph $$g(x) = \sin(x + \frac{\pi}{2})$$ from $$f(x) = \sin(x)$$?

Accepted Answer

Horizontal shift left $$\frac{\pi}{2}$$ units

Question 8

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = 0.5\sin(x)$$?

Accepted Answer

Vertical compression by a factor of 0.5

Question 9

Which transformation would result in the graph $$g(x) = \sin(-x)$$?

Accepted Answer

Reflection about the y-axis

Question 10

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = \sin(x) - 1$$?

Accepted Answer

Vertical shift down 1 unit

Question 11

A function $$f(x) is $$reflected about the x-axis and then shifted up 2 units. Which of the following represents the new function?

Accepted Answer

$$-f(x) + 2$$

Question 12

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = \sin(\frac{x}{2})$$?

Accepted Answer

Horizontal stretch by a factor of 2

Question 13

Which transformation would result in the graph $$g(x) = 2\sin(x)$$?

Accepted Answer

Vertical stretch by a factor of 2

Question 14

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = \sin(x - 2)$$?

Accepted Answer

Horizontal shift right 2 units

Question 15

Which transformation would produce the graph $$g(x) = -\sin(-x)$$ from $$f(x) = \sin(x)$$?

Accepted Answer

Reflection about both x-axis and y-axis

Question 16

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = \sin(x + \pi)$$?

Accepted Answer

Horizontal shift left $$\pi$$ units

Question 17

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = \sin(-x) + 1$$?

Accepted Answer

Reflection about the y-axis and vertical shift up 1 unit

Question 18

Which transformation would result in the graph $$g(x) = \sin(3x)$$?

Accepted Answer

Horizontal compression by a factor of $$\frac{1}{3}$$

Question 19

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$g(x) = -2\sin(x)$$?

Accepted Answer

Reflection about the x-axis and vertical stretch by a factor of 2

Graphing Techniques: Transformations of Functions

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