Horizontal Shifts in Sine Graphs

The video tutorial covers horizontal shifting of trigonometric graphs, explaining the difference between shifting and stretching. It demonstrates how to use a calculator to graph functions, determine step size, and plot the graph. The tutorial concludes with an analysis of graph characteristics such as amplitude, range, domain, and period.

What is the primary focus of this lesson compared to previous ones?

• Vertical stretching of graphs

• Horizontal shifting of graphs

• Vertical shifting of graphs

• Graph compression

What is the first step in using a calculator to plot a sine graph with a horizontal shift?

• Select the graph mode

• Enter the equation

• Choose the table option

• Set the interval

How is the step size for plotting a sine graph determined?

• By dividing the period by 2

• By dividing the period by 4

• By multiplying the period by 2

• By multiplying the period by 4

What is a limitation of using a calculator to plot a sine graph?

• It does not account for horizontal shifts

• It may miss some critical points due to shifts

• It cannot display the graph visually

• It cannot plot negative values

What is the amplitude of a sine graph?

• The maximum x-value

• The distance from the resting position

• The total length of the graph

• The minimum y-value

What is the range of a sine graph that has not been stretched or compressed?

• From -1 to 0

• From -2 to 2

• From -1 to 1

• From 0 to 1

What does the domain of a graph refer to?

• The maximum amplitude

• The period of the graph

• The interval of x-values given

• The range of y-values

How does a horizontal shift affect the period of a sine graph?

• It doubles the period

• It halves the period

• It does not affect the period

• It triples the period

What happens to the turning points of a sine graph when it is shifted horizontally by 30 degrees?

• They move 30 degrees to the right

• They remain unchanged

• They move 30 degrees to the left

• They move 60 degrees to the right

What is the period of a sine graph that has been shifted horizontally but not stretched or compressed?

• 180 degrees

• 360 degrees

• 90 degrees

• 270 degrees