Understanding Absolute Value Functions

The video tutorial explains how to graph an absolute value function, starting with an introduction to the absolute value graph and the problem setup. It discusses the restrictions imposed by absolute value, different definitions, and interpretations. The tutorial then covers graph transformation based on absolute value properties and concludes with the final graph explanation and common mistakes students make.

What is the initial step when graphing an absolute value function?

• Start with the absolute value graph

• Identify the x-intercepts

• Determine the range

• Find the slope

What restriction is implied by the absolute value in the function?

• f(x) must be less than zero

• f(x) must be greater than zero

• y must be negative

• x must be positive

Which of the following is a definition of absolute value?

• The negative value of a number

• The square of a number

• The distance from zero

• The sum of a number and its opposite

What is the most technical definition of absolute value discussed?

• The positive value of a number

• The distance from zero

• The sum of a number and its opposite

• The value of a number without regard to its sign

When is f(x) equal to y in the context of absolute value?

• When x is positive

• When x is negative

• When y is greater than or equal to zero

• When y is less than zero

What transformation occurs when y is less than zero in the graph?

• The graph shifts down

• The graph reflects across the y-axis

• The graph shifts up

• The graph reflects across the x-axis

What happens to the graph when y is positive?

• It remains the same as the original graph

• It shifts to the left

• It shifts to the right

• It reflects across the y-axis

How does the graph change when y is negative?

• It remains unchanged

• It shifts down

• It shifts up

• It reflects across the x-axis

What is the result of applying the absolute value to the left-hand side of the equation?

• The graph is reflected across the x-axis

• The graph is reflected across the y-axis

• The graph is shifted to the right

• The graph is unchanged

What common mistake do people make when graphing absolute value functions?

• Forgetting to label the axes

• Using the wrong scale

• Applying the absolute value to the wrong side

• Ignoring the x-intercepts