Question

The graph is supposed to show f(x) = 3 sin (x/4+1) - 1/2. Which of the following are correctly represented in the graph? Select two of the following that apply.

Answer 1

1. pi/2 and 3pi/2

2. f(x)=cotx

3. domain: -inf<x<inf, x does not equal pi/2+npi, where n is an integer

range: -inf<y<inf

4. f(x)=cotx and f(x)=secx

5. It is true, because the cosine function has a period of 2pi

6. f(x) has no zeros and f(x) has a period of 2pi

7. right pi/4

8. 4pi

9. It has an amplitude of 1/4 and it is a horizontal shift of the parent function pi/3 units left

10. the amplitude and the vertical shift

Explanation:

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Answer 2

Options a and b

Explanation:

Amplitude of the graph = 3 but shown correctly

Hence option a is right

There is a vertical shift of 1/2 down. Shown correctly

Option b is right

Horizontal shift is 1 unit to the left after adjusting x for x/4. Shown incorrectly

OPtion c is not right

Period is 8 pi not shown correctly

OPtion d is wrong.

Horizontal expansion is not shown at all for x/4

Hence option e is wrong.