Question 1

Given the function $$y = 4 \sec\left(\frac{1}{2}x\right)$$, what is the stretching factor?

Accepted Answer

$$4$$

Question 2

For the function $$y = 4 \sec\left(\frac{1}{2}x\right)$$, what is the period?

Accepted Answer

$$4\pi$$

Question 3

Where are the vertical asymptotes for $$y = 4 \sec\left(\frac{1}{2}x\right)$$ within one period?

Accepted Answer

$$-\pi, \pi, 3\pi$$

Question 4

If the function $$y = a \sec(bx)$$ has a period of $$6\pi$$, what is the value of $$b$$?

Accepted Answer

$$\frac{1}{6}$$

Question 5

Which transformation occurs when the function $$y = \sec(x) is $$changed to $$y = 4 \sec\left(\frac{1}{2}x\right)$$?

Accepted Answer

Vertical stretch by 4 and horizontal stretch by 2

Question 6

A real-world application: The intensity $$I of a $$light beam varies as $$I = 4 \sec\left(\frac{1}{2}x\right)$$, where $$x is $$the angle in radians. What is the minimum positive value of $$x$$ where the intensity is undefined?

Accepted Answer

$$\pi$$

Question 7

Which of the following is the general formula for the vertical asymptotes of $$y = 4 \sec\left(\frac{1}{2}x\right)$$?

Accepted Answer

$$x = (2n+1)\pi$$

Question 8

If $$y = 4 \sec\left(\frac{1}{2}x\right)$$ models the voltage in an AC circuit, what is the voltage when $$x = 0$$?

Accepted Answer

$$4$$

Question 9

Which of the following best describes the range of $$y = 4 \sec\left(\frac{1}{2}x\right)$$?

Accepted Answer

$$(-\infty, -4] \cup [4, \infty)$$

Question 10

Suppose $$y = 4 \sec\left(\frac{1}{2}x\right) is $$used to model the height of a Ferris wheel seat above the ground as a function of angle $$x. If $$the seat is at its lowest point at $$x = 0$$, what is the maximum height within one period?

Accepted Answer

$$4$$

Analyzing the Graph and Properties of a Secant Function

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