Add an absolute value function and quadratic to find the domain

The video tutorial explains how to add two functions, F(x) and G(x), and discusses the resulting function's domain. It highlights that both functions have domains of all real numbers, and thus their sum also has a domain of all real numbers. The tutorial emphasizes understanding the properties of absolute value and quadratic functions and how they affect the domain when combined.

What is the result of adding the functions F(x) = |x + 3| - 1 and G(x) = x^2 - 7?

• x^2 + |x + 3| - 6

• x^2 + |x + 3| - 8

• x^2 - |x + 3| - 8

• x^2 + |x + 3| + 8

Which of the following terms can be combined when simplifying the expression F(x) + G(x)?

• The x terms from each function

• The coefficients of x

• The constants from each function

• The absolute value and the quadratic term

What is the domain of the function F(x) = |x + 3| - 1?

• x ≠ 0

• x < 0

• x > 0

• All real numbers

Why does the combined function F(x) + G(x) have a domain of all real numbers?

• Because the combined function is a polynomial

• Because both functions are linear

• Because both functions have no restrictions on their domains

• Because the combined function is a constant

How can you verify the domain of the combined function F(x) + G(x)?

• By solving the equation for x

• By graphing the function

• By finding the derivative

• By calculating the integral