Question 1

Given the graph in Image 1, which of the following is a possible equation for the function using the sine function?

Accepted Answer

$$y = 4 \sin\left(\frac{\pi}{6}x\right)$$

Question 2

Given the graph in Image 1, which of the following is a possible equation for the function using the cosine function?

Accepted Answer

$$y = 4 \cos\left(\frac{\pi}{6}x - \pi\right)$$

Question 3

Which of the following best describes the amplitude and period of the function in Image 1?

Accepted Answer

Amplitude: 4, Period: $$12$$

Question 4

For the function $$y = 4 \sin\left(\frac{\pi}{6}x\right)$$, what is the value of $$y$$ when $$x = 3$$?

Accepted Answer

$$y = 2$$

Question 5

Which of the following equations matches the reciprocal function shown in Image 2?

Accepted Answer

$$y = 4 \sec\left(x\right)$$

Question 6

Which of the following statements about the graph in Image 2 is correct?

Accepted Answer

The graph has vertical asymptotes at $$x = n\pi$$, where $$n is an $$integer.

Question 7

If $$y = 4 \sin\left(\frac{\pi}{6}x\right)$$, what is the equation of its reciprocal function?

Accepted Answer

$$y = 4 \csc\left(\frac{\pi}{6}x\right)$$

Question 8

Which transformation would shift the graph of $$y = 4 \sin\left(\frac{\pi}{6}x\right) to $$the right by 3 units?

Accepted Answer

$$y = 4 \sin\left(\frac{\pi}{6}(x-3)\right)$$

Question 9

If the period of $$y = a \sin(bx) is$$ $$12$$, what is the value of $$b$$?

Accepted Answer

$$b = \frac{2\pi}{12}$$

Question 10

Which of the following best describes the relationship between the graphs of $$y = 4 \sin\left(\frac{\pi}{6}x\right)$$ and $$y = 4 \cos\left(\frac{\pi}{6}x - \pi\right)$$?

Accepted Answer

They are identical graphs.

Question 11

Suppose a temperature varies as $$T(t) = 8 \cos\left(\frac{\pi}{60}t\right) + 112. $$What is the temperature after $$t = 90$$ minutes?

Accepted Answer

$$T = 104$$

Question 12

Which of the following is the correct reciprocal function for $$y = 4 \cos\left(\frac{\pi}{6}x\right)$$?

Accepted Answer

$$y = 4 \sec\left(\frac{\pi}{6}x\right)$$

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