Analyzing 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 new vertex, and determining 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 understanding these concepts even without a graph.

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

• To determine the domain and range

• To identify the x-intercepts

• To calculate the area under the curve

• To find the slope of the function

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

• A circle

• A straight line

• A parabola

• A V-shape

What does a horizontal translation of a graph involve?

• Moving the graph up or down

• Moving the graph left or right

• Changing the slope of the graph

• Reflecting the graph over the x-axis

Where is the new vertex located after translating the graph left 3 units and down 2 units?

• (-3, -2)

• (2, 3)

• (3, 2)

• (-2, -3)

How does the graph of an absolute value function change after translation?

• It becomes a straight line

• It rotates around the origin

• It shifts to a new position

• It remains unchanged

What is the domain of an absolute value function?

• All positive numbers

• Only integers

• All real numbers

• All negative numbers

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

• Because it has a constant slope

• Because it is a quadratic function

• Because it is a linear function

• Because it has no division by zero

What determines the range of an absolute value function?

• The y-intercepts

• The x-intercepts

• The slope of the function

• The vertex of the graph

If the graph of an absolute value function opens upwards, what can be said about its range?

• y is less than or equal to a certain value

• y is greater than or equal to a certain value

• y is equal to zero

• y is undefined

What is the range of the function if the vertex is at (-3, -2) and the graph opens upwards?

• y ≤ -2

• y ≥ 3

• y ≥ -2

• y ≤ 3