Understanding Absolute Value Function Transformations

The video tutorial explains how to graph an absolute value function in standard form. It covers identifying the values of a, h, and k, and describes the transformations they cause, such as reflection, vertical compression, and shifts. The tutorial demonstrates graphing the function using software and manually, verifying the transformations and final graph with a table of values.

What is the standard form of an absolute value function?

• y = a(x + h) - k

• y = a|x + h| - k

• y = a|x - h| + k

• y = a(x - h) + k

What effect does a negative 'a' value have on the graph of an absolute value function?

• It stretches the graph horizontally.

• It reflects the graph across the x-axis.

• It compresses the graph vertically.

• It shifts the graph to the left.

How does the graph change when 'h' is positive?

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.

• The graph shifts down.

What is the effect of a positive 'k' value on the graph?

• The graph shifts down.

• The graph shifts up.

• The graph shifts right.

• The graph shifts left.

What is the vertex of the function y = -1/2|x - 3| + 4?

• (3, 4)

• (0, 0)

• (4, 3)

• (-3, -4)

What happens to the point (2, 2) after applying a vertical compression by a factor of 1/2 and reflection?

• (2, 1)

• (2, -1)

• (-2, -1)

• (-2, 1)

After applying the transformations, what is the new position of the vertex?

• (0, 0)

• (1, 2)

• (3, 4)

• (6, 8)

Which points are used to avoid fractions when graphing by hand?

• (4, 4) and (-4, 4)

• (1, 1) and (-1, 1)

• (2, 2) and (-2, 2)

• (3, 3) and (-3, 3)

What is the final step in graphing the absolute value function by hand?

• Reflecting the graph across the y-axis.

• Shifting the graph left and down.

• Shifting the graph right and up.

• Stretching the graph vertically.

How can you verify the accuracy of the final graph?

• By checking the slope.

• By using a table of values.

• By measuring the angles.

• By comparing with a circle.