Understanding Absolute Value Graph Transformations

The video tutorial explains how to graph the absolute value of a function, f(x), by reflecting the parts of the graph that are below the x-axis across the x-axis. It begins with an introduction to the concept, followed by an analysis of a table of values for f(x) and |f(x)|. The tutorial then provides a graphical explanation of how to reflect the negative parts of f(x) to obtain the graph of |f(x)|. Two examples are given to illustrate the process, emphasizing that the graph of |f(x)| will never be below the x-axis.

What happens to the graph of a function when you take the absolute value of the function?

• It reflects all parts below the x-axis across the x-axis.

• It shifts upwards by one unit.

• It shifts to the right by one unit.

• It becomes a straight line.

Which part of the function's graph is affected when taking the absolute value?

• The parts below the x-axis.

• The entire graph shifts upwards.

• The parts above the x-axis.

• The entire graph shifts downwards.

How do you graph the absolute value of a function?

• Reflect the parts of the graph below the x-axis across the x-axis.

• Rotate the graph 90 degrees.

• Reflect the entire graph across the y-axis.

• Shift the graph upwards by two units.

What is the result of reflecting a negative part of a function's graph across the x-axis?

• The graph shifts to the right.

• The graph shifts to the left.

• The negative part becomes positive.

• The graph remains unchanged.

Why will the graph of the absolute value of a function never be below the x-axis?

• Because the function values are always positive.

• Because the graph is shifted upwards.

• Because the graph is rotated.

• Because the graph is shifted to the right.

In the context of graphing absolute values, what does reflecting across the x-axis mean?

• Shifting the graph upwards.

• Flipping the graph over the x-axis.

• Rotating the graph 180 degrees.

• Shifting the graph to the left.

What is the first step in graphing the absolute value of a function?

• Identify the parts of the graph above the x-axis.

• Rotate the graph 90 degrees.

• Shift the entire graph upwards.

• Identify the parts of the graph below the x-axis.

What happens to the graph of f(x) when f(x) is negative and you take the absolute value?

• The negative values are reflected above the x-axis.

• The graph shifts to the right.

• The graph shifts downwards.

• The graph remains unchanged.

What is the purpose of reflecting parts of a graph across the x-axis when graphing absolute values?

• To make the graph symmetrical.

• To rotate the graph 180 degrees.

• To ensure all function values are non-negative.

• To shift the graph to the left.

What is the final outcome when graphing the absolute value of a function?

• A graph that is a straight line.

• A graph that is a circle.

• A graph that is entirely below the x-axis.

• A graph that is entirely above the x-axis.