Functions and Relations G7

Introduction:

A relation is any set of ordered pairs (x,y).

Ex. x squared plus y squared equals r squared. This is the equation of a circle with center(0,0) and of radius r. A function is a relation of the form y equals f(x) in which for one value of x there’s only one value of y. There are three main types of functions. A constant function f( x) equals 2, a linear function f(x) equals 2x- 4 and a quadratic function f( x) equals x swuaref -1. The graph of a constant function is a horizontal line with y intercept at (0,c) while the graph of a linear function is a straight line of slope 2 and y-intercept at -4. The graph of a quadratic function is a parabola.

Example 1: Find the equation of a circle with center at (0,0) at of radius 5.
Solution 1: x squared plus y squared equals 5 squared. Therefore x squared plus y squared equals 25.

Example 2: if f( x ) equals 2x-3, find f(3) and f(2k) .
Solution 2: f3) equals 2(3)-3 equals 3 and f(2k) equals 2(2k) -3 equals 4k-3.

Example 3: Describe the graphs of f(x) equals 5 and f(x) equals 2x -3.
Solution 3: a horizontal line passing through the point (0,5). A straight line passing through (0,-3) and with a slope of 2.

Conclusion:

We learned a little bit about relations and functions today. The majority of calculus math is all about functions and relations.