Define Function, Function Notation, Domain and Range

This video tutorial by Brian McLogan introduces precalculus students to functions, covering their characteristics, graph analysis, and the definition of a function. It explains the vertical line test, function notation, and the concepts of domain and range, providing a comprehensive overview of these foundational topics.

What is a key characteristic of a continuous graph?

• It is always symmetrical.

• It has breaks or jumps.

• It can be drawn without lifting the pencil.

• It has multiple y-values for a single x-value.

Which test is used to determine if a graph represents a function?

• Vertical Line Test

• Slope Test

• Symmetry Test

• Horizontal Line Test

In a table, what indicates that a set of values does not represent a function?

• An x-value maps to multiple y-values.

• Each x-value maps to a unique y-value.

• All y-values are positive.

• The table has more x-values than y-values.

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

• The input value

• The output value

• The slope of the function

• The name of the function

In function notation, what does the expression inside the parentheses represent?

• The output value

• The rule of the function

• The input value

• The range of the function

What is the domain of a function?

• The set of all y-values

• The set of all x-values

• The highest point on the graph

• The lowest point on the graph

How is the range of a function defined?

• The set of all x-values

• The difference between the highest and lowest x-values

• The set of all y-values

• The difference between the highest and lowest y-values

What happens to the domain of a function if a term in the denominator equals zero?

• The domain includes all real numbers.

• The domain includes only positive numbers.

• The domain excludes the value that makes the denominator zero.

• The domain includes only negative numbers.

When is a function's domain restricted by a radical?

• When the radical is in the numerator

• When the radical is in the denominator

• When the radical results in a positive number

• When the radical results in a negative number

What is the domain of the function y = x + 3?

• x ≠ 3

• x < 0

• x > 0

• All real numbers