Graphing Absolute Value Functions: Key Concepts and Techniques

The video tutorial covers graphing absolute value functions, starting with the parent function y = |x|. It explains the properties of absolute value functions, including domain, range, and vertex. The tutorial then delves into transformations such as vertical and horizontal translations, vertical dilation, and reflections. Several examples are provided to illustrate these concepts, showing how to graph transformed absolute value functions and analyze changes in domain, range, and vertex.

What is the domain of the absolute value parent function y = |x|?

• -infinity to 0

• 0 to 1

• -infinity to infinity

• 0 to infinity

Where is the vertex of the absolute value parent function y = |x|?

• (0, 1)

• (-1, 1)

• (1, 1)

• (0, 0)

In the formula y = a|x - h| + k, what does the 'a' represent?

• Vertical translation

• Horizontal dilation

• Horizontal translation

• Vertical dilation

If the value of 'a' in y = a|x - h| + k is between 0 and 1, what happens to the graph?

• It moves left

• It moves right

• It compresses vertically

• It stretches vertically

What is the new range of the function f(x) = |x| + 2?

• -2 to infinity

• 0 to infinity

• 2 to infinity

• -infinity to 2

What is the vertex of the function f(x) = |x| + 2?

• (2, 2)

• (0, 2)

• (0, 0)

• (2, 0)

How does the graph of f(x) = |x - 4| transform from the parent function?

• Moves left 4 units

• Moves down 4 units

• Moves up 4 units

• Moves right 4 units

What is the vertex of the function f(x) = |x - 4|?

• (4, 0)

• (0, 4)

• (-4, 0)

• (0, 0)

In the function f(x) = 2|x| - 5, what is the effect of the coefficient 2?

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 2

• Horizontal stretch by a factor of 2

• Horizontal compression by a factor of 2

What is the range of the function f(x) = -3|x - 3| + 1?

• -infinity to 0

• -infinity to 1

• 0 to infinity

• -3 to infinity