Understanding Linear and Absolute Value Functions

The video tutorial explains absolute value functions, highlighting their algebraic properties and how they always yield positive values. It covers graphing these functions as piecewise functions, detailing the role of boundary lines and vertices. The tutorial emphasizes the continuity of absolute value functions and provides an example to illustrate the concept, focusing on the boundary line where the function changes.

What is the output of an absolute value function when the input is negative?

• A negative value

• Zero

• The same negative value

• A positive value

How are absolute value functions typically graphed?

• As a piecewise function

• As a cubic function

• As a quadratic function

• As a single linear function

What is the role of the boundary line in a piecewise function?

• It marks the maximum value of the function

• It indicates where the function changes

• It shows the average value of the function

• It is the starting point of the function

What is a vertex in the context of piecewise functions?

• The average value of the function

• The minimum or turning point of the function

• The point where the function starts

• The highest point of the function

How do absolute value functions behave in terms of continuity?

• They have gaps between different segments

• They are continuous without jumps

• They have sudden jumps in Y values

• They are discontinuous at the vertex

What happens to the Y values in an absolute value function?

• They decrease continuously

• They remain constant

• They jump between segments

• They change smoothly without gaps

In the given example, what is the x-value of the boundary line?

• x = 0

• x = 1

• x = -1

• x = -2

What type of linear function is present from x = -∞ to x = -2 in the example?

• A quadratic function

• An increasing linear function

• A decreasing linear function

• A constant linear function

What happens to the linear function at x = -2 in the example?

• It starts increasing

• It becomes a constant function

• It remains unchanged

• It starts decreasing