Understanding Functions and Their Domains

The video tutorial reviews the concept of functions, focusing on their inputs and outputs. It explains the domain of a function, using examples like f(x) = 2/x and g(y) = √(y-6) to illustrate how domains are determined. The tutorial also explores a unique function with a limited domain, emphasizing the importance of understanding where a function is defined.

What is the output of the function f(x) = 2/x when the input is 3?

• 1/3

• 3

• 2/3

• 3/2

Why is the function f(x) = 2/x undefined for x = 0?

• Because x cannot be negative

• Because 2/0 is undefined

• Because 0 is not a real number

• Because 2 is not divisible by 0

What is the domain of the function f(x) = 2/x?

• All real numbers except 0

• Only negative numbers

• All real numbers

• Only positive numbers

For the function g(y) = √(y-6), what must be true for y?

• y must be greater than or equal to 6

• y must be equal to 6

• y must be a negative number

• y must be less than 6

What is the domain of g(y) = √(y-6)?

• y < 6

• y ≥ 6

• y > 0

• y = 6

In the function h(x) defined as 1 if x = pi and 0 if x = 3, what is the domain?

• Only x = pi

• Only x = 3

• x = pi and x = 3

• All real numbers

What is the output of h(x) when x = pi?

• pi

• 0

• Undefined

• 1

What happens if you input a number other than pi or 3 into h(x)?

• The output is the input number

• The output is 0

• The output is 1

• The function is undefined

Why is understanding the domain of a function important?

• It helps in solving equations

• Not all functions are defined for all real numbers

• It simplifies calculations

• It determines the range

Which of the following is NOT a possible domain for a function?

• All real numbers

• Only positive numbers

• Only imaginary numbers

• Only whole numbers