The x and y intercepts of a graph are points of intersection of the graph with the x axis and the y axis respectively. This a tutorial with examples and detailed solutions on how to find these points.
Example 1: Find the x and the y intercepts of the graph of function f defined by
f(x) =  3 x + 9
Solution to Example 1

Since a point on the y axis has x coordinate equal to zero, to find the y interecpt, we set x to zero and find the y coordinate which is f(0).
f(0) = 3(0) + 9 = 9

A point on the x axis has y coordinate equal to 0, to find the x intercept, we set y = f(x) = 0 and solve for x
f(x) = 3 x + 9 = 0

Solve for x.
x = 3

The x and y intercepts of the graph of f are
x intercept: (3 , 0)
y intercept: (0 , 9)
Example 2: Find the x and the y intercepts of the graph of the 2 variable equation given by
(x  1)^{ 2} + (y  2)^{ 2} = 16
Solution to Example 2

We first set x = 0 to find the y intrecpt.
(0  1)^{ 2} + (y  2)^{ 2} = 16

Solve for y
1 + (y  2)^{ 2} = 16
(y  2)^{ 2} = 15
y = 2 + sqrt(15) and y = 2  sqrt(15)

Set y = 0 and solve for x
x = 1 + sqrt(12) and x = 1  sqrt(12)

The x and y intercepts of the graph of the given equation are
x intercepts: (1 + sqrt(12) , 0) and ((1  sqrt(12) , 0)
y intercepts: (0 , 2 + sqrt(15)) and (0 , 2  sqrt(15))

The graph shown below is that of the given equation. Examine the x and y intercepts and compare to those calculated. Note that the x and y intercepts may be determined graphically.
