1.2.4 Introduction to Functions

Key Objectives • Graph points in the coordinate plane. • Locate points in the coordinate plane. • Generate and graph ordered pairs. Key Terms • A coordinate plane is formed by the intersection of two perpendicular number lines (axes) in a plane. The point of intersection is the zero on each number line. • The two perpendicular number lines on a coordinate plane are called the axes . • The x - and y -axes divide the coordinate plane into four regions. Each region is called a quadrant . • An ordered pair is a pair of numbers that can be used to locate a point on a coordinate plane. The first number in an ordered pair is called the x -coordinate and the second number in an ordered pair is called the y -coordinate . • A function can be represented by an equation with two variables where the value of y (the output ) is determined by the value of x (the input ). Example 1 Graphing Points in the Coordinate Plane The coordinate plane is formed by the intersection of two perpendicular number lines, called axes, that intersect at 0 on each number line. This point of intersection is called the origin. The horizontal number line is called the x -axis, and the vertical number line is called the y -axis. • The horizontal axis on a coordinate plane is called the x -axis . • The vertical axis on a coordinate plane is called the y -axis . • The point where the axes intersect in a coordinate plane is called the origin . Each point or position on a coordinate plane can be described by an an ordered pair, written as ( x, y ). The x -value in an ordered pair is called the x -coordinate, and the y-value in an ordered pair is called the y -coordinate. Points on a coordinate plane are named with a capital letter. To graph an ordered pair ( x, y ) on a coordinate plane, begin at the origin and then move x -units to the left or right (depending on whether the x -coordinate is positive or negative) along the x -axis. Then, move y -units up or down (depending on whether the y -coordinate is positive or negative) from that position on the x -axis. The resulting location is the position of the point ( x, y ).

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