Understanding Trigonometric Graph Transformations

What is the primary focus of this video tutorial?

• Learning about geometry

• Graphing trigonometric functions

• Solving algebraic equations

• Understanding calculus concepts

In the function y = a sin(fx - h) + v, what does 'a' represent?

• Phase shift

• Frequency

• Period

• Amplitude

How is the period of a trigonometric function determined?

• By the amplitude

• By the vertical shift

• By the formula 2π divided by the absolute value of frequency

• By the horizontal shift

What is the effect of a horizontal phase shift in a trigonometric function?

• It changes the amplitude

• It alters the frequency

• It moves the graph up or down

• It shifts the graph left or right

What is the first step in graphing the function y = 2cos(x + π/2) + 1?

• Graph the basic cosine function

• Apply the vertical shift

• Determine the frequency

• Calculate the period

When graphing y = 2cos(x), what does the '2' indicate?

• The graph is shifted up by 2 units

• The frequency is 2

• The graph is shifted left by 2 units

• The amplitude is 2

How does adding π/2 to x in the function y = 2cos(x + π/2) affect the graph?

• It increases the amplitude

• It decreases the frequency

• It shifts the graph to the left by π/2

• It shifts the graph to the right by π/2

What transformation is applied last in the function y = 2cos(x + π/2) + 1?

• Vertical shift

• Horizontal shift

• Frequency change

• Amplitude adjustment

What is the final vertical shift applied to the function y = 2cos(x + π/2) + 1?

• Up by 1 unit

• Down by 1 unit

• Up by 2 units

• Down by 2 units

What is the overall effect of the transformations on the graph of y = 2cos(x + π/2) + 1?

• It remains unchanged

• It becomes a linear function

• It becomes a sine function

• It becomes a tangent function