Graphing a Transformed Cosine Function

The video tutorial explains how to sketch the graph of a cosine function with transformations. It covers identifying parameters like amplitude, period, phase shift, and vertical shift. The tutorial demonstrates graphing the function step-by-step, including plotting key points and using graphing tools for accuracy.

What is the initial step in sketching the graph of the given function?

• Determining the y-intercepts

• Calculating the derivative

• Finding the x-intercepts

• Identifying the function's parameters

What is the amplitude of the function f(θ) = -2cos(θ - π/4) + 1?

• 4

• 2

• 3

• 1

How does a negative amplitude affect the graph of a cosine function?

• It shifts the graph upwards

• It shifts the graph downwards

• It reflects the graph across the midline

• It stretches the graph vertically

What is the period of the function f(θ) = -2cos(θ - π/4) + 1?

• 2π

• 4π

• π

• π/2

What is the phase shift of the function f(θ) = -2cos(θ - π/4) + 1?

• Left π/4

• Right π/2

• Right π/4

• Left π/2

What is the vertical shift of the function f(θ) = -2cos(θ - π/4) + 1?

• Down 2 units

• Down 1 unit

• Up 1 unit

• Up 2 units

What is the midline of the function f(θ) = -2cos(θ - π/4) + 1?

• y = 2

• y = 0

• y = 1

• y = -1

What is the pattern of the cosine function after considering the negative amplitude?

• Midline, Maximum, Midline, Minimum, Midline

• Maximum, Minimum, Maximum, Minimum, Maximum

• Minimum, Midline, Maximum, Midline, Minimum

• Maximum, Midline, Minimum, Midline, Maximum

How do you determine the maximum value of the function f(θ) = -2cos(θ - π/4) + 1?

• Divide the amplitude by the midline

• Multiply the amplitude by the midline

• Subtract the amplitude from the midline

• Add the amplitude to the midline

Which tool can be used to graph the function online?

• A tool that selects two maximum points

• A tool that selects a minimum and a maximum point

• A tool that selects two minimum points

• A tool that selects a midline and a maximum point