How to determine the domain of the sum of two functions

The video tutorial covers the process of adding functions, emphasizing the need for like terms and common denominators. It explains how to simplify expressions by rewriting them with a common denominator and demonstrates combining fractions. The tutorial also delves into identifying the domain of functions, highlighting restrictions such as division by zero and square roots of negative numbers. The instructor provides examples and clarifies domain constraints, ensuring students understand how to determine valid input values for functions.

What is necessary for combining functions?

• They must have the same variables.

• They must be linear functions.

• They must be like terms.

• They must have the same coefficients.

What is the least common denominator of 3 and 4?

• 4

• 3

• 12

• 7

Why is it important to have a common denominator when adding fractions?

• To combine the fractions into a single expression.

• To make the numerators equal.

• To simplify the multiplication process.

• To ensure the fractions are equivalent.

What are the two main restrictions on the domain of a function?

• Values that make the function undefined and values that make the function negative.

• Values that make the denominator zero and values that make the square root negative.

• Values that make the function positive and values that make the function zero.

• Values that make the numerator zero and values that make the function positive.

Which value cannot be in the domain if it makes the denominator zero?

• Any positive number

• Any negative number

• Any number that results in zero

• Any number greater than one

What is the domain of the function if X + 3 must be greater than or equal to 0?

• X must be greater than or equal to -3

• X must be less than or equal to -3

• X must be greater than or equal to 3

• X must be less than or equal to 3

How can you determine the domain of a function with a square root?

• Ensure the expression inside the square root is a fraction.

• Ensure the expression inside the square root is zero.

• Ensure the expression inside the square root is negative.

• Ensure the expression inside the square root is positive.