Exploring Graphing Absolute Value Functions

This video tutorial explains how to graph absolute value functions, starting with the parent function and moving on to translations. It covers vertical and horizontal shifts, writing equations for these translations, and understanding the role of the vertex and slope. Advanced graphing techniques, including handling negative slopes and fractions, are also discussed.

What shape does the graph of an absolute value function typically have?

• Circular

• V-shaped

• Linear

• U-shaped

If an absolute value function is translated 2 units up, how is this represented in the equation?

• y = |x| - 2

• y = |x|

• y = |x + 2|

• y = |x| + 2

What does the 'H' in the equation 'y = M|x - H| + K' represent?

• Vertical shift

• Slope

• Stretch factor

• Horizontal shift

How do you represent a shift of 9 units to the right in an absolute value equation?

• y = |x + 9|

• y = |x| - 9

• y = |x - 9|

• y = |x| + 9

What is the vertex form of an absolute value function?

• y = M(x - H)^2 + K

• y = M|x - H| + K

• y = M|x + H| + K

• y = M(x + H)^2 + K

If the vertex of an absolute value function is at (1, 3), how is this represented in the equation?

• y = |x - 1| + 3

• y = |x + 1| - 3

• y = |x - 3| + 1

• y = |x + 1| + 3

In the equation 'y = M|x - H| + K', what does 'K' represent?

• Vertical shift

• Stretch factor

• Horizontal shift

• Slope

What effect does a negative slope outside the absolute value bars have on the graph?

• It shifts the graph to the right.

• It inverts the graph to open downwards.

• It makes the graph wider.

• It shifts the graph upwards.

How does a slope of 2 outside the absolute value bars affect the graph?

• It shifts the graph 2 units up.

• It makes the graph narrower.

• It shifts the graph 2 units down.

• It makes the graph wider.

What does a slope of -1/2 outside the absolute value bars do to the graph?

• It makes the graph narrower.

• It shifts the graph 1/2 unit down.

• It makes the graph wider.

• It shifts the graph 1/2 unit up.