What students always forget when writing the domain

The video tutorial explains how to find the domain of functions with both radicals and rational expressions. It highlights common student mistakes, such as focusing only on radicals and forgetting rational function restrictions. The instructor provides tips for solving domain problems, including setting radicals greater than or equal to zero and denominators equal to zero. The tutorial emphasizes the importance of finding the intersection of domains and uses graphical methods to illustrate this concept. The video aims to enhance understanding of domain restrictions, especially when dealing with multiple functions.

What are the two main restrictions to remember when finding the domain of a rational expression?

• You can't subtract zero and you can't take the cube root of a positive number.

• You can't add zero and you can't take the square root of a positive number.

• You can't multiply by zero and you can't take the cube root of a negative number.

• You can't divide by zero and you can't take the square root of a negative number.

When dealing with multiple restrictions in a function, what is a helpful strategy?

• Write out each function and its restriction separately.

• Ignore the radical and focus on the denominator.

• Only consider the restriction with the largest number.

• Combine all restrictions into a single equation.

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

• Set the expression under the square root greater than or equal to zero.

• Set the expression under the square root less than zero.

• Set the expression under the square root equal to zero.

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

What is the purpose of setting the denominator equal to zero in a rational function?

• To find the values that make the function defined.

• To find the values that make the function undefined.

• To find the maximum value of the function.

• To find the minimum value of the function.

What is the next step after finding the domain restrictions for each function separately?

• Add the restrictions together.

• Find the intersection of the restrictions.

• Multiply the restrictions together.

• Subtract the restrictions from each other.

How can you visually represent the domain restrictions to find their intersection?

• Use a single graph with different colors for each function.

• Use a single graph with the same color for each function.

• Use separate graphs for each function without colors.

• Use a pie chart to represent the restrictions.

What symbol is used to combine the domains of two functions?

• A union symbol.

• A division symbol.

• A minus sign.

• A plus sign.