Combining and Analyzing Functions

This video tutorial explains how to create new functions by adding and subtracting existing ones. It begins with a review of what a function is, emphasizing the relationship between inputs and outputs. The tutorial then demonstrates how to evaluate functions with specific examples. It further explores combining functions through addition and subtraction, providing detailed examples and graphing illustrations. The lesson concludes by summarizing the process of forming new functions from existing ones.

What is the term used to describe the set of all possible inputs for a function?

• Graph

• Domain

• Range

• Output

What is the range of a function?

• The difference between the highest and lowest outputs

• The set of all possible inputs

• The set of all possible outputs

• The average of all outputs

If a function gives the same output for different inputs, what does this indicate?

• The function is a constant function

• The function is linear

• The function has multiple outputs

• The function is not well-defined

How do you determine the output of a function at a specific input?

• By graphing the function

• By integrating the function

• By substituting the input into the function

• By finding the derivative of the function

When combining two functions by addition, what is the resulting function called?

• The quotient of the functions

• The difference of the functions

• The sum of the functions

• The product of the functions

What happens to the graph of a function when you add another function to it?

• It shifts vertically

• It shifts horizontally

• It remains unchanged

• It reflects over the x-axis

What must be done when subtracting one function from another to ensure accuracy?

• Distribute a negative sign across the second function

• Multiply both functions by a constant

• Add a constant to both functions

• Divide both functions by a constant

What is a key consideration when subtracting functions?

• Ensuring the functions have the same domain

• Adding a constant to both functions

• Distributing the negative sign correctly

• Ensuring the functions are of the same type

What is the result of combining a quadratic function and an absolute value function?

• A new function with unique characteristics

• An exponential function

• A polynomial function

• A linear function

What is the visual result of combining two functions on a graph?

• A single line

• A graph that is always linear

• A new graph that combines characteristics of both

• Two separate graphs