Understanding Absolute Value Functions

The video tutorial explains how to find the domain and range of an absolute value function. It covers the concept of graph translation, identifying the vertex, and understanding the domain and range. The domain of an absolute value function is all real numbers, while the range depends on the vertex and the direction the graph opens. The tutorial emphasizes that even without a graph, one can determine these properties by analyzing the function's equation.

What is the primary goal when analyzing an absolute value function?

• To identify the x-intercepts

• To calculate the area under the curve

• To determine the domain and range

• To find the slope of the function

How does the graph of an absolute value function change when it is translated left 3 units?

• It moves upwards

• It shifts to the left

• It shifts to the right

• It moves downwards

What type of translation occurs when the graph is moved down 2 units?

• Horizontal translation

• Vertical translation

• No translation

• Diagonal translation

What happens to the graph of an absolute value function when it is translated vertically?

• It shifts left or right

• It rotates

• It moves up or down

• It becomes wider

What is the effect of a horizontal translation on the graph of an absolute value function?

• It changes the slope

• It shifts the graph left or right

• It moves the graph up or down

• It reflects the graph

Where is the new vertex located after the graph is translated?

• At (3, -2)

• At (-3, -2)

• At (3, 2)

• At (0, 0)

What shape does the graph of an absolute value function typically have?

• L-shaped

• S-shaped

• V-shaped

• U-shaped

What is the domain of an absolute value function?

• Only integers

• All real numbers

• All negative numbers

• All positive numbers

Why is the domain of an absolute value function all real numbers?

• Because it includes division by zero

• Because it can take any real number as input

• Because it includes negative square roots

• Because it is only defined for positive numbers

What determines the range of an absolute value function?

• The y-intercepts

• The x-intercepts

• The vertex of the graph

• The slope of the function