Graph Transformations and Sine Functions

The video tutorial explains the concept of horizontal stretch transformations in graphing functions. It covers two cases: when the scaling factor 'a' is greater than 1, resulting in a horizontal shrink, and when 'a' is a fraction between 0 and 1, leading to a horizontal stretch. The tutorial uses the sine function as an example to illustrate these transformations, showing how the graph changes in each scenario. The video concludes with a summary of the transformation rules.

What is the main focus of a horizontal stretch transformation?

• Altering the vertical position of the graph

• Changing the amplitude of the graph

• Shifting the graph along the y-axis

• Modifying the horizontal scale of the graph

In the context of horizontal stretch, what does the parameter 'a' represent?

• The scaling factor along the y-axis

• The scaling factor along the x-axis

• The horizontal shift of the graph

• The vertical shift of the graph

When 'a' is greater than 1, what happens to the graph of f(ax) compared to f(x)?

• The graph is shrunk horizontally

• The graph is stretched horizontally

• The graph is stretched vertically

• The graph is shifted to the right

In the example of sine(2x), what is the value of sine(2x) when x is pi/4?

• 0

• 1

• -1

• 0.5

How many cycles does sine(2x) complete in the interval 0 to 2pi?

• Two cycles

• One cycle

• Half a cycle

• Three cycles

What is the general effect on the graph of f(x) when a > 1?

• The graph is shifted upwards

• The graph is shrunk horizontally

• The graph is reflected over the x-axis

• The graph is stretched vertically

When 'a' is a fraction between 0 and 1, what happens to the graph of f(ax) compared to f(x)?

• The graph is stretched horizontally

• The graph is reflected over the y-axis

• The graph is shifted to the left

• The graph is shrunk vertically

In the example of sine(x/2), what is the value of sine(x/2) when x is 2pi?

• -1

• 1

• 0

• 0.5

How many cycles does sine(x/2) complete in the interval 0 to 4pi?

• One cycle

• Two cycles

• Three cycles

• Half a cycle

What is the general effect on the graph of f(x) when 0 < a < 1?

• The graph is stretched vertically

• The graph is stretched horizontally

• The graph is shifted downwards

• The graph is reflected over the x-axis