Graphing Negative Cosine Functions

The video tutorial explains how to graph the function y = -cos(pi*x) + 1.5 using an interactive widget. It begins by discussing the properties of the cosine function, including its period and oscillation between maximum and minimum points. The tutorial then covers how to calculate the period of cosine(pi*x) and the effect of a negative sign, which flips the graph. Finally, it demonstrates how to apply a vertical shift of 1.5 to the graph, resulting in the final graph of the function.

What is the purpose of the interactive widget mentioned in the video?

• To calculate derivatives

• To graph trigonometric functions

• To solve algebraic equations

• To find the area under a curve

What is the maximum value of cos(pi * x) when x = 0?

• 0.5

• 0

• 1

• -1

How do you determine the period of cos(pi * x)?

• By dividing 2 pi by the coefficient of x

• By adding 2 pi to the coefficient of x

• By subtracting 2 pi from the coefficient of x

• By multiplying 2 pi by the coefficient of x

What is the period of the function cos(pi * x)?

• 2 pi

• 1

• pi

• 2

What effect does the negative sign have on the graph of cos(pi * x)?

• It shifts the graph to the right

• It shifts the graph to the left

• It flips the graph vertically

• It stretches the graph horizontally

What happens to the graph when you apply a negative sign to cos(pi * x)?

• The graph is shifted downwards

• The graph is flipped vertically

• The graph is flipped horizontally

• The graph is shifted upwards

What is the effect of adding 1.5 to the function -cos(pi * x)?

• It shifts the graph 1.5 units to the left

• It shifts the graph 1.5 units upwards

• It shifts the graph 1.5 units downwards

• It shifts the graph 1.5 units to the right

How does the graph of -cos(pi * x) + 1.5 differ from -cos(pi * x)?

• It is shifted 1.5 units upwards

• It is compressed horizontally

• It is shifted 1.5 units downwards

• It is stretched vertically

What is the new midline of the graph after adding 1.5 to -cos(pi * x)?

• y = 1.5

• y = -1.5

• y = 0

• y = 1

What is the range of the function -cos(pi * x) + 1.5?

• [0, 3]

• [1, 2]

• [0.5, 2.5]

• [-1, 1]