Operations on Functions

Operations on functions involves combining two or more functions by adding, subtracting, multiplying, or dividing them together. For addition and subtraction, you simply combine like terms, making sure to pay attentiong to signs, especially when subtracting. Multiplying could involve using tactics like FOILing, distributive property, or multiplying polynomials. For division, it is important to be aware of the domain of the denominator.

Adding and Finding Domain
Subtracting and Finding Domain
Multiplying and Finding Domain
Dividing and Finding Domain

Evaluate Functions

When asked to evaluate a function, it simply means to replace the variable in the function with the given value or expression, and simplify. This is typically a simple task, especially when evaluating for a numeric value. The advantage of using function notation is that you can clearly see the ordered pair, so you know what value you plugged into the independent variable to get the response variable.

Evaluate Linear Funct.
Evaluate Power Funct.

Composite Functions

Composite functions are functions that are composed of another function. Basically, you are plugging one function into another function, and simplifying the answer. The domain for these is the domain of the function being plugged in and the domain of the answer.

Composite Functions and Finding Domain
Surface Area as a Function of Time

Inverse Functions

Functions are inverses if and only if f(g(x))=x and g(f(x))=x. To find the inverse, switch the x and y variables and solve for x. The domain of the original function is equal to the range of the inverse, and the range of the original function is equal to the domain of the inverse.

Verify if Inverse Functions
Find Inverse - Linear
Find Inverse - Power
Find Inverse - Rational

Difference Quotient

The difference quotient is used in Calculus to define the derivative. For now, the videos just show how to use the difference quotient, and derivatives will not be expanded any further. It is useful for applications such as velocity of an object and optimization problems.

Difference Quotient - Linear
Difference Quotient - Quadratic