In this lesson, you will learn about Functions starting with a review of relations. You will cover the vertical line test which graphically tests for functions as well as a new function notation. Four examples at the end of the lecture make sure you fully understand the new concepts. A function is a relation between a given set of elements called the domain and a set of elements called the codomain.
A function is a
relation in which each element of the domain is paired with exactly
one element of the range.
A relation is a
function if and only if its graph passes the vertical line test:
any vertical line passes through the graph at no more than one
If f is a
function, we use function notation to describe f. For example, we
could write f(x) = 3x + 2. The function f can be evaluated for
specific values of x, such as 5. We write f(5) = 3(5) + 2 + 17.
Thus, f(5) is an element of the range of f.
For the function
f(x), x represents the independent variable and f(x) represents the
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.