Graphing Transformations and Properties

This video tutorial covers the transformation of sinusoidal functions, focusing on stretching and shrinking them both vertically and horizontally. It reviews the basic graphs of sine and cosine functions, explains how to adjust amplitude and period, and demonstrates how to determine equations from given graphs. The tutorial concludes with a practical example of sketching a graph from a given equation, emphasizing the effects of negative amplitude and period adjustments.

What is the amplitude of a basic sine or cosine function?

• 0

• 1

• 2

• π

How does multiplying the function by a value 'a' affect the graph?

• It shifts the graph horizontally.

• It changes the period of the graph.

• It stretches or shrinks the graph vertically.

• It rotates the graph.

What happens to the graph when 'a' is negative?

• The graph flips upside down.

• The graph shifts to the right.

• The graph becomes narrower.

• The graph becomes wider.

If 'b' is greater than 1, what happens to the period of the graph?

• The period increases.

• The period decreases.

• The period remains the same.

• The graph flips upside down.

What is the relationship between 'b' and the number of waves in the interval from 0 to 2π?

• 'b' is the amplitude.

• 'b' is the number of waves.

• 'b' is the frequency.

• 'b' is the period.

How do you determine the amplitude of a graph?

• By measuring the width of one wave.

• By measuring the distance between two peaks.

• By measuring the height from the midline to the peak.

• By counting the number of waves.

What is the period of a graph if 'b' is 2?

• π

• 2π

• π/2

• 2

How do you find the value of 'b' if the period is given?

• Multiply the period by 2π.

• Divide 2π by the period.

• Subtract the period from 2π.

• Add 2π to the period.

What is the first step in sketching a graph given an equation with a negative 'a'?

• Shift the graph to the right.

• Flip the graph upside down.

• Stretch the graph horizontally.

• Rotate the graph.

When sketching a graph, how do you determine the scaling of the x-axis?

• By using the frequency.

• By using the amplitude.

• By using the phase shift.

• By using the period.