Operations of Functions with Domain

The video tutorial covers the combination of functions and the determination of their domains. It begins with an introduction to functions and their domains, followed by detailed explanations of how to add, subtract, multiply, and divide functions. Each operation is demonstrated with examples, highlighting the importance of domain restrictions. Advanced examples are provided to illustrate simplification techniques. The tutorial concludes with further examples and a summary of key concepts.

What is the domain of a linear function like F(x) = x - 3?

• Negative Infinity to Infinity

• 0 to Infinity

• Negative Infinity to 0

• 1 to Infinity

Why is it important to use parentheses when subtracting functions?

• To avoid subtracting only part of the expression

• To ensure the correct order of operations

• To make the expression look neat

• To simplify the expression

What method can be used to multiply functions larger than binomials?

• FOIL Method

• Graphical Method

• Box Method

• Distributive Property

When dividing functions, what must be considered regarding the denominator?

• It must be greater than zero

• It must be a positive integer

• It must be a whole number

• It must not equal zero

How can you simplify a rational expression like (x^2 - 4x + 3) / (x - 3)?

• By multiplying both by a common factor

• By adding a constant to both numerator and denominator

• By factoring the numerator and canceling common terms

• By dividing both by a common factor

What is the domain of the function F(x) = 2 / (2x + 1)?

• Negative Infinity to -1/2

• Negative Infinity to 0

• 0 to Infinity

• Negative Infinity to Infinity

What is the result of multiplying 3√x by itself?

• 6x

• x

• 3x

• 9x

What is the domain of the function H(x) = 3√x?

• 1 to Infinity

• 0 to Infinity

• Negative Infinity to Infinity

• Negative Infinity to 0

How do you determine the domain of a function resulting from division?

• By ensuring the denominator is not zero

• By ensuring both numerator and denominator are positive

• By ensuring both numerator and denominator are integers

• By ensuring the numerator is not zero

What is the domain of the function G(x) = x^2 - 4x + 3?

• Negative Infinity to Infinity

• 0 to Infinity

• Negative Infinity to 0

• 1 to Infinity