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 Description  
 Graph of a Function:  The set of all the points on a coordinate plane whose coordinates makes the rule of function true.
The graphs below illustrate graphs of functions. The x-intercept of each graph is the value at which the graph crosses the x-axis. For example, for Figure A, the x-intercept is 9/5 or . The x-intercept for Figure B is 0. Can you tell what the x-intercept is for Figure C?

Similarly, the y-intercept for each graph is the value at which the graph crosses the y-axis. For example, for Figure A, the y-intercept is 9. Can you tell what the y-intercepts are for Figures B and C?

     
 
y = -5x+9
Figure A
 
Figure B
 Figure C


You can check that the equation you have graphed is a function by using the vertical line test. If you can draw a vertical line on the same coordinate plane as your graph such that the vertical line intersects your graph in more than one point, the equation is not a function--it is called a relation.

Example:


The red curve in the figure above shows the graph of the circle x2 + y2 = 9. A vertical line (e.g. y = -1.5) intersects the graph of the circle at two separate points. Thus, a cicle is not a function but a relation.

The reason the vertical line test works: The intersections between a vertical line and a graph of the relation show all the possible y values that are the output values for a certain x value. For a function, we want every x value to "produce" exactly one y value--that is, we are looking for only one intersection between the graph of the relation and a vertical line drawn anywhere on the graph of the relation. If the vertical line intersects the graph of the relation more than once, then it reveals that a single x value is paired with more than one y value, and therefore the relation cannot be a function.