Understanding the Coordinate Plane and Functions

Axes: ejes   Increasing: creciente   Gradient: pendiente   Grid: cuadrícula   Decreasing: decreciente   Quadrant: cuadrante   Domain: dominio   Range: recorrido   Slope: pendiente

The coordinate plane, or Cartesian plane, is formed by the horizontal line and vertical line meeting at the point 0.

The horizontal line is called the x-axis.

The vertical line is called the y-axis.

The point where the two lines meet is the origin.

Plotting Points: Starting at the origin, we move 2 units to the right along the x-axis, then move vertically up 1 unit. We describe the location of this point as the ordered pair, also called the coordinates of the point. The x-value is also called the abscissa and the y-value is called the ordinate.

The x and y axes divide the plane into four quarters. Each of these is called a quadrant.

A function is a relation between two variables called x and y, in which x is the independent variable, y is the dependent variable, and every x-value is related to one and only one y-value (because there is only one value for x).

The domain of the function is the set of all real numbers of the variable x that it can take.

The range is the set of all values that the function takes when x takes values in the domain.

If the graph of a function is going up from left to right, it is an increasing function.

If it is going down from left to right, it is a decreasing function.

If at the left of a point the function is increasing, and at the right it is decreasing, it is the maximum.

If the function first decreases and then increases, it is the minimum.

A continuous function is a function whose graph can be drawn without lifting the pencil from the notebook. Otherwise, the function is discontinuous.

To Draw the Graph of a Function:

• Write a table of values
• Calculate the value of y for each x
• Draw a suitable grid
• Plot the pairs and join them with a line

There are some graphs which are very useful, such as horizontal graphs. The y-coordinate is always the same.

You calculate the equation of a straight line by finding the gradient and the y-intercept.

All straight lines have a similar expression: y = mx + n.

- m is the gradient and indicates how steep it is.

- n is the y-intercept, the point where the line cuts the y-axis.