Graphing Trig Functions

Describe the horizontal shift for the function @@y=\cos(x-\frac{3\pi}{4})@@.

• left 3π / 4

• right 3π / 4

• left π / 3

• right π / 4

Write the equation for a cosine function with a vertical shift of -3 and an amplitude of 2.

• @@y=2rac{1}{2} ext{cos}(x)-3@@

• @@y=2 ext{cos}(x)+3@@

• @@y=2 ext{cos}(x)-3@@

• @@y=3 ext{cos}(x)-2@@

• \(\frac{\pi}{2}\) to the left

• \(\frac{\pi}{2}\) to the right

• \(\pi\) to the right

• \(0\)

Where is the midline for @@y=2\cos\left(\frac{1}{3}x+\frac{\pi}{6}\right)+2@@?

• +1

• +2

• +3

• +4

What is another name for a phase shift?

• Vertical Shift

• Horizontal Shift/Translation

• Phase Translation

• Time Shift

What is the effect of a negative sign in front of a cosine function?

• It reflects the graph across the x-axis.

• It shifts the graph to the right.

• It stretches the graph vertically.

• It changes the amplitude of the graph.

How do you determine the midline of a trigonometric function?

• The midline is the horizontal line that runs through the average of the maximum and minimum values of the function.

• The midline is the vertical line that passes through the maximum value of the function.

• The midline is the line that connects the maximum and minimum points of the function.

• The midline is the line that represents the amplitude of the function.

Write an equation for the cosine function with amplitude 3, period 2π, phase shift of π, and vertical shift of 5.

• y=3\cos\left(x-\pi\right)+5

• y=2\cos\left(x-\frac{\pi}{2}\right)+4

• y=3\cos\left(x+\pi\right)+2

• y=5\cos\left(x-\pi\right)+3

What is the equation of the graph that has an amplitude of 2 and is a sine function?

• y = 2 sin x

• y = sin x

• y = 3 sin x

• y = 2 cos x

How does a vertical shift affect the graph of a trigonometric function?

• A vertical shift moves the entire graph up or down without changing its shape.

• A vertical shift stretches the graph vertically, altering its amplitude.

• A vertical shift reflects the graph across the x-axis.

• A vertical shift compresses the graph horizontally, changing its period.