3.3 Geometry

There is also a connection between functions (see section 4.2.10) and the coordinate plane. If a function
is graphed in the coordinate plane, the function can be understood in different and useful ways.
Consider the function defined by

7 6

J(x)=-—x+—.

5 5

If the value of the function,f(x), is equated with the variable y, then the graph of the function in
the xy-coordinate plane is simply the graph of the equation

7 6

y=-—x+—

5 5

shown above. Similarly, any function J(x) can be graphed by equating y with the value of the function:

y = f(x).

So for any x in the domain of the function f, the point with coordinates (x,j(x)) is on the graph

off, and the graph consists entirely of these points.

As another example, consider a quadratic polynomial function defined by j(x)= x2 -1. One can plot

several points (x,j(x)) on the graph to understand the connection between a function and its graph:

X

三二o-1

1

3

IO

I

I

y

． (-2,3) 3

2

.(2 3) '

(-1,0)

1

(1,0)

• 
  

  (^2) - 1

  
  

  !十
  (^0 ,}^1 ) (^2) X