Creating New Functions by Adding and Subtracting

This lesson teaches 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 lesson then demonstrates how to combine functions through addition and subtraction, using examples to illustrate the process. Graphical representations are used to show the results of these combinations. The lesson concludes by summarizing the key points of creating new functions from existing ones.

What is a function in mathematical terms?

• A relationship where each input has multiple outputs

• A random collection of numbers

• A set of inputs with no outputs

• A relationship where each input has one output

What is the result of evaluating the function f(x) at x = 4?

• The output is 8

• The output is 10

• The output is 6

• The output is 4

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

• f plus g of x

• f minus g of x

• f divided by g of x

• f times g of x

What is the output of f plus g of x when evaluated at x = 3?

• 11

• 8

• 14

• 5

What must be done when subtracting one function from another?

• Distribute the negative sign

• Add the functions together

• Ignore the negative sign

• Multiply the functions

What is the result of combining p(x) and q(x) by subtraction?

• p minus q of x

• p divided by q of x

• p times q of x

• p plus q of x

What types of functions were combined in the final example?

• A polynomial and an absolute value function

• Two quadratic functions

• Two linear functions

• A logarithmic and an exponential function