Understanding Absolute Value Functions

The video tutorial explains how to graph a piecewise function, specifically focusing on the absolute value function y = |x - 2| + 1 for the domain where X is less than or equal to 2. It describes the characteristics of absolute value functions, noting that they are continuous and only exist in the positive Y-axis. The tutorial provides a step-by-step guide to graphing the function for X ≤ 2, including creating a table of values to visualize the linear shape of the graph.

What is the domain of the function y = |x - 2| + 1 that we are graphing?

• x < 2

• x ≥ 2

• x ≤ 2

• x > 2

Why does a piecewise absolute value function only appear in the positive y-axis?

• Because it is a discontinuous function

• Because it is a quadratic function

• Because all y-values must be positive

• Because it is a linear function

What is the vertex of the general absolute value function y = |x|?

• (0, 0)

• (2, 2)

• (1, 1)

• (-1, -1)

How does the general absolute value function y = |x| behave?

• It is a constant function

• It has a vertex and two linear segments

• It is a quadratic function

• It is a cubic function

What is the y-value when x = 2 for the function y = |x - 2| + 1?

• 3

• 0

• 1

• 2

What is the y-value when x = 0 for the function y = |x - 2| + 1?

• 4

• 2

• 1

• 3

What is the shape of the graph for the function y = |x - 2| + 1 for x ≤ 2?

• A V-shape

• A parabola

• A circle

• A straight line