Understanding Absolute Value Functions

This video tutorial explains the vertex form of absolute value functions, detailing the roles of variables a, h, and k. It covers two methods for graphing these functions: plotting the vertex and using transformations. The tutorial includes a step-by-step example of each method, emphasizing the importance of symmetry and reflection in graphing. The video concludes with a comprehensive transformation method, illustrating how to apply horizontal and vertical shifts, stretches, and reflections to graph absolute value functions.

What is the vertex form of an absolute value function?

• f(x) = a|x + h| - k

• f(x) = ax^2 + bx + c

• f(x) = a|x - h| + k

• f(x) = a(x - h)^2 + k

Why can't the variable 'a' be zero in the vertex form of an absolute value function?

• It would turn the function into a quadratic function.

• It would make the function undefined.

• It would make the function a constant function.

• It would make the function a linear function.

What does the variable 'a' represent in the vertex form of an absolute value function?

• Stretch or shrink and reflection

• Vertex location

• Vertical translation

• Horizontal translation

How does the variable 'h' affect the graph of an absolute value function?

• It shifts the graph up or down.

• It shifts the graph left or right.

• It reflects the graph over the x-axis.

• It stretches the graph vertically.

What is the effect of a positive 'k' on the graph of an absolute value function?

• The graph becomes narrower.

• The graph shifts down.

• The graph shifts up.

• The graph reflects over the y-axis.

Where is the vertex of an absolute value function located in vertex form?

• (h, a)

• (a, k)

• (0, 0)

• (h, k)

What is the line of reflection in the graph of an absolute value function?

• y = k

• x = 0

• x = h

• y = a

What is the first step in graphing an absolute value function using the vertex method?

• Find the line of reflection

• Plot the vertex

• Reflect over the x-axis

• Perform vertical stretch

In the vertex method, after plotting the vertex, what is the next step?

• Perform vertical translation

• Reflect the vertex over the y-axis

• Perform horizontal translation

• Find another point and reflect it

In the transformation method, what is the first transformation applied?

• Reflection over x-axis

• Horizontal translation

• Vertical stretch

• Vertical translation