Understanding Domain and Range Part 2

In the previous post, we have learned the graphical representation of domain and range. The domain of the function f is the shadow or projection of the graph of f to the x-axis (see the red segment in the figure below). The range of f is the projection of the graph of f to the y-axis (see the green segment in the figure below). In this post, we are going to learn how to analyze equations of functions and determine their domain and range without graphing.

domain and range

If a graph of a function is projected to the x-axis, the projection is the set of x-coordinates of the graph. A single point (a,0) on the projection means a point on the graph exists. The existence of a point implies that f(a) exists. This means that the function is defined at x = a. In effect, the domain of a function is the set of x-coordinates that makes the function defined. In what follows, we learn some examples to illustrate this concept.  » Read more

Understanding Domain and Range Part 1

The domain of a function is the set of x-coordinates of the points in the function. The range of the function f is the set of y-coordinates of the points in the function. So if we have a function f with points (-3, -2), (-1, 3), (2, 3), and (5,4), then the domain of the function f is the set {-3, -1, 2, 5} and the range of f is the set {-2, 3, 4). Graphically, we can say that the domain is the  “projection” of the points to the x-axis (see red points in the following figure).

domain

The range of f is the projection of the points to the y-axis (see green points in the following figure).  » Read more

Understanding Radian Measure

A circle O with radius 1 unit has its center placed at the origin. Let A be its intersection with the x-axis at (1,0) and P be another point on its circumference. If we move P along its circumference, then we can determine the distance traveled by P. If we let A be the starting point of P as it moves counterclockwise, then the distance traveled by P is equal to the length of arc AP represented by the red arc in the following figure.

radian 2

To be able to know the length of arc AP, first, we must know the total distance traveled by P from A going counterclockwise and back to A  (i.e. complete revolution). That is, we need to find the circumference of the circle. Since a unit circle has radius 1 unit, its circumference C is  » Read more

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