Exploring Domain and Range of Continuous Graphs

The video tutorial covers the concepts of domain and range in continuous graphs. It explains how to determine the domain and range using a pencil trick, scanning from left to right for domain and bottom to top for range. The tutorial provides examples with different graph types, including V-shaped graphs, circles, parabolas, and vertical lines, and explains how to express these in interval notation.

What is the first step in finding the domain of a continuous graph?

• Scan your pencil from right to left along the x-axis

• Scan your pencil from left to right along the x-axis

• Scan your pencil from top to bottom along the y-axis

• Scan your pencil from bottom to top along the y-axis

When finding the range of a graph, in which direction should you scan your pencil?

• From bottom to top along the y-axis

• From right to left along the x-axis

• From top to bottom along the y-axis

• From left to right along the x-axis

What does an arrow on a graph typically indicate about the values?

• The values are imaginary

• The values continue indefinitely

• The values are undefined

• The values stop at a certain point

In interval notation, how is the domain of a V-shaped graph that extends infinitely in both directions represented?

• (-∞, -∞)

• (-∞, ∞)

• (-∞, 0)

• (0, ∞)

For a circular graph, what is the range if the highest point on the y-axis is 3 and the lowest point is -3?

• (-∞, ∞)

• [0, 3]

• (-3, 3)

• [-3, 3]

What does it mean if a graph's domain is described as 'all real numbers'?

• The graph has no x-values

• The graph includes every possible x-value

• The graph only includes positive x-values

• The graph only includes negative x-values

How is the range of a graph with arrows extending infinitely in both directions represented in interval notation?

• (-∞, ∞)

• (-∞, 0)

• (-∞, -∞)

• (0, ∞)

What is the highest y-value in the range of an upside-down U-shaped graph if the tip is at y = 4?

• y = -4

• y = 4

• y = 2

• y = 0

In a vertical graph, what is the domain if the x-value is always 2?

• x = 0

• x = 2

• x = -2

• x = ∞

For a vertical graph, what is the range if the graph extends infinitely in both directions?

• [0, ∞]

• [-∞, -∞]

• [-∞, 0]

• [-∞, ∞]