Sine Function Transformations and Properties

The video tutorial explains how to graph the function f(x) = 1 + 3sin(π/2(x-1)). It covers determining transformation values a, b, d, and c, which affect amplitude, period, phase shift, and vertical shift. The tutorial guides viewers through plotting key points and completing the graph over the interval. It also provides instructions for using graphing tools to accurately represent the function.

What is the amplitude of the function f(x) = 1 + 3 sin(π/2(x - 1))?

• 1

• 3

• 0

• π/2

If the coefficient of sine is negative, what transformation occurs?

• No transformation

• Reflection across the midline

• Vertical shift

• Horizontal shift

How is the period of the function calculated?

• π divided by the coefficient of x

• 2π divided by the coefficient of x

• π times the coefficient of x

• 2π times the coefficient of x

What is the vertical shift of the function f(x) = 1 + 3 sin(π/2(x - 1))?

• Up 1

• Down 3

• Down 1

• Up 3

Where does the graph of the function start due to the phase shift?

• x = -1

• x = 1

• x = 2

• x = 0

What is the maximum value of the function f(x) = 1 + 3 sin(π/2(x - 1))?

• 4

• 1

• 3

• 0

How many sub-intervals is the period divided into when graphing?

• 3

• 2

• 4

• 5

At which x-value does the function return to the midline after reaching the maximum?

• x = 4

• x = 5

• x = 3

• x = 2

What is the pattern followed when a is positive in the sine function?

• Midline, minimum, midline, maximum, midline

• Minimum, midline, maximum, midline, minimum

• Midline, maximum, midline, minimum, midline

• Maximum, midline, minimum, midline, maximum

Which tool is used to graph the sine function accurately?

• Calculator

• Ruler

• Graphing tool

• Protractor