Understanding Absolute Value Graphs

The video tutorial introduces the concept of absolute value graphs, starting with the basic definition and representation of y = |x|. It explains how absolute value graphs can be understood by considering only positive values and how they 'bounce' at the axis. The tutorial then explores variations by modifying the expression within the absolute value and discusses the resulting graph behavior. Finally, it examines the effects of shifts outside the absolute value, demonstrating how these shifts can introduce negative components to the graph.

What is the basic shape of the graph y = |x|?

• A straight line

• A V-shape

• A parabola

• A circle

How does the graph of y = |x - 1| differ from y = |x|?

• It shifts right by 1 unit

• It shifts down by 1 unit

• It shifts left by 1 unit

• It shifts up by 1 unit

What happens to the graph of y = |x| when x is negative?

• It remains unchanged

• It becomes a straight line

• It reflects over the x-axis

• It reflects over the y-axis

What is the equation of the left branch of y = |x|?

• y = -x + 1

• y = x + 1

• y = -x

• y = x

How does subtracting a constant outside the absolute value affect the graph?

• It shifts the graph right

• It shifts the graph down

• It shifts the graph up

• It shifts the graph left

What is the effect of the equation y = |x| - 1 on the graph?

• The graph shifts left by 1 unit

• The graph shifts down by 1 unit

• The graph shifts right by 1 unit

• The graph shifts up by 1 unit

What is the equation of the right branch of y = |x - 1|?

• y = -x + 1

• y = x + 1

• y = -x - 1

• y = x - 1

In the graph of y = |x|, what happens at the origin?

• The graph bounces off the y-axis

• The graph bounces off the x-axis

• The graph intersects the x-axis

• The graph intersects the y-axis

What is the equation of the left branch of y = |x| - 1?

• y = -x + 1

• y = x + 1

• y = -x - 1

• y = x - 1

How do you determine the equation of a flipped branch in an absolute value graph?

• Subtract a constant from x

• Add a constant to x

• Multiply x by -1

• Divide x by -1