


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
xintercept of each graph is the value at which the graph crosses the xaxis.
For example, for Figure A, the xintercept is 9/5 or . The
xintercept for Figure B is 0. Can you tell what the xintercept is for Figure
C?
Similarly, the yintercept for each graph is the value at which
the graph crosses the yaxis. For example, for Figure A, the yintercept is 9.
Can you tell what the yintercepts 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 functionit is called a relation.
Example:
The red curve in the figure above shows the graph of the circle x^{2} + y^{2} = 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 valuethat 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.


