Understanding Function Domains and Ranges

This video tutorial explains how to find the domain of a function using different approaches. It covers finding the domain when given an equation, focusing on avoiding division by zero and handling square roots. The video also discusses determining the domain from a graph by analyzing x-values. Key concepts include using interval notation and understanding the implications of even and odd roots.

What is the primary concern when finding the domain of a function?

• Ensuring the function is continuous

• Avoiding division by zero

• Minimizing the range

• Maximizing the range

When given a rational function, what should you do to find its domain?

• Set the entire function equal to zero

• Set the denominator not equal to zero

• Set the function greater than zero

• Set the numerator equal to zero

Why can't the denominator of a rational function be zero?

• It would make the function quadratic

• It would make the function linear

• It would make the function undefined

• It would make the function continuous

What is the domain of the function y = 3/(2x - 1)?

• All real numbers except x = 1/2

• All real numbers except x = 2

• All real numbers

• All real numbers except x = 0

What is a key restriction when dealing with square roots in functions?

• The value under the square root must be negative

• The value under the square root can be any real number

• The value under the square root must be zero

• The value under the square root must be positive

How do you find the domain of a function with a square root?

• Set the expression under the square root not equal to zero

• Set the expression under the square root equal to zero

• Set the expression under the square root less than zero

• Set the expression under the square root greater than zero

What is the domain of the function y = √(5x - 3)?

• x ≥ 3/5

• x ≤ 3/5

• x > 3/5

• x < 3/5

What is the difference between even and odd roots regarding domain?

• Odd roots cannot have negative values under the root

• Odd roots must have positive values under the root

• Even roots can have negative values under the root

• Even roots cannot have negative values under the root

What is the domain of the cube root of a negative number?

• It is negative

• It is undefined

• It is real

• It is positive

How can you determine the domain from a graph?

• By analyzing the slope

• By analyzing the x-values

• By analyzing the intercepts

• By analyzing the y-values