Understanding Domains and Ranges of Functions

This video tutorial explains how to determine the domain and range of a function by examining sets, graphs, equations, and mappings. It emphasizes the importance of understanding the definitions of domain and range, and provides examples to illustrate how to identify them. The tutorial also covers how to visually determine domain and range from graphs and discusses the specific case of square root functions, highlighting the need to consider restrictions on inputs and outputs.

What is the domain of a function?

• The set of all integers

• The set of all real numbers

• The set of all acceptable inputs

• The set of all possible outputs

Why can't zero be used as an input in some functions?

• Because it is not an integer

• Because it is not a positive number

• Because it results in division by zero

• Because it is not a real number

What is a common misunderstanding about the domain of a function?

• That it includes only negative numbers

• That any number can be used as an input

• That it includes only integers

• That it includes only positive numbers

In the example function, what are the acceptable inputs?

• 0, 2, -1, 3, 6

• Only positive numbers

• Only negative numbers

• All real numbers

What is the range of the function f(x) = 3x + 1?

• All integers

• All real numbers

• Only negative numbers

• Only positive numbers

How do you determine the domain of a function from a graph?

• By looking at the y-axis

• By looking at the x-axis

• By looking at the z-axis

• By looking at the graph's color

What is the range of a graph if the lowest y-value is -3?

• All real numbers greater than or equal to -3

• All real numbers

• All real numbers less than -3

• All integers

Why must the expression under a square root be non-negative?

• Because it must be a positive number

• Because it must be a real number

• Because it must be an integer

• Because square roots of negative numbers are undefined

What is the domain of the function f(x) = 3√(2x - 1)?

• All values greater than or equal to 1/2

• All real numbers

• All integers

• All positive numbers

What is the range of the function f(x) = 3√(2x - 1)?

• All real numbers

• All real numbers greater than or equal to zero

• All integers

• All positive numbers