In mathematics, a function is a relation between sets that assigns to each element of a first set, exactly one element of the second set. A graph of a function is a visual representation of the relationship between the two sets. In order to complete an equation for a function graphed above, one must first identify the type of function. The type of function is often determined by the form of the graph.
Types of Functions
The three most common types of functions are linear, quadratic, and exponential. Linear functions are graphed as a straight line, and can be described by a simple equation of the form y=mx+b, where m is the slope of the line and b is the y-intercept. Quadratic functions are graphed as a parabola, and can be described by a more complex equation of the form y=ax2+bx+c, where a, b, and c are constants. Exponential functions are graphed as an exponential curve, and can be described by an equation of the form y=ax+b, where a and b are constants.
Finding the Equation
Once the type of function is determined, one can complete the equation by analyzing the graph. For linear functions, the slope and y-intercept can be determined by inspecting the graph. The equation can then be written as y=mx+b, where m and b are the determined values. For quadratic and exponential functions, the constants can be determined by finding the x- and y-intercepts of the graph. The equation can then be written as y=ax2+bx+c for quadratic functions and y=ax+b for exponential functions, where a, b, and c are the determined values.
Examples
For example, the graph below shows a parabola, indicating that the equation is of the form y=ax2+bx+c. By finding the x- and y-intercepts, one can determine the constants and complete the equation: y=2x2+4x-1.
In conclusion, completing an equation for the function graphed above requires one to first identify the type of function, and then use the graph to determine the constants of the equation. With a bit of practice, one can become proficient in completing equations for functions graphed above.
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