Subtract two quadratic equations to determine the domain

The video tutorial explains the process of subtracting functions, highlighting common mistakes such as failing to distribute negative signs across all terms in the second function. It demonstrates the correct method by inserting grouping symbols and distributing the negative sign, leading to the correct combination of like terms. The tutorial also covers the concept of domains, emphasizing that the domain of the result remains the same as the original functions when adding or subtracting. The video concludes by noting that this principle also applies to multiplication.

What is a common mistake students make when subtracting functions?

• Forgetting to add the functions

• Not distributing the negative sign across the entire function

• Multiplying instead of subtracting

• Ignoring the coefficients of the terms

When distributing the negative sign in function subtraction, what happens to the signs of the terms?

• They all become positive

• They remain the same

• They all become negative

• They change to the opposite sign

After correctly distributing the negative sign, what is the simplified form of the expression X^2 - 3X + 1 - (X^2 + X - 5)?

• -4X + 6

• X^2 - 4X + 6

• 3X - 5

• -2X - 4

What is the domain of the resulting function after subtracting two quadratic functions?

• Only integers

• Only negative numbers

• All real numbers

• Only positive numbers

Does the domain change when adding, subtracting, or multiplying functions with all real numbers?

• No, it remains all real numbers

• Yes, it becomes only positive numbers

• Yes, it becomes more restricted

• Yes, it becomes only integers