Function Notation and Graph Behavior

This tutorial covers the characteristics of functions, focusing on key vocabulary such as roots, domain, and range. It includes two examples: analyzing a logarithmic function using a graphing calculator and identifying increasing and decreasing intervals on a graph. The video emphasizes understanding graph behavior and using function notation.

What is the term used for the point where a graph crosses the x-axis?

• Y-intercept

• Slope

• X-intercept

• Vertex

Which of the following represents the set of all possible x-values of a function?

• Range

• Asymptotes

• Domain

• Intercepts

How do we read the domain of a function?

• From top to bottom

• From left to right

• From right to left

• From bottom to top

What is the term for invisible boundary lines that a graph approaches but does not cross?

• Intercepts

• Asymptotes

• Vertices

• Endpoints

What does the notation f(x) or g(x) represent in function notation?

• The slope

• The x-value

• The y-value

• The intercept

In the graph of G(x) = log(2x), what is the x-intercept?

• 0, 1

• 2, 0

• 0.5, 0

• 1, 0

Does the graph of G(x) = log(2x) have a y-intercept?

• Yes, at (0, 0)

• No, it does not exist

• Yes, at (1, 0)

• Yes, at (0, 1)

In the second example, what is the interval where the graph is increasing?

• (-∞, -1)

• (-1, 1)

• (1, ∞)

• (-∞, ∞)

What are the x-intercepts of the graph in the second example?

• (0, 0), (1, 0)

• (-1, 0), (1, 0)

• (-2, 0), (1, 0)

• (-2, 0), (0, 0), (2, 0)

What is the domain of the graph in the second example?

• (-∞, 0)

• (-∞, ∞)

• (-2, 2)

• (0, ∞)