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Finding the x and y Intercepts

In order to find the x and y intercepts of a graph, we need to remember that we’re looking for where the graph crosses the x and y axes.  If the graph crosses the x-axis, then that point has a y-coordinate of 0 since all points on the x-axis have y-coordinate 0.  To find an x-intercept, merely substitute 0 for y, and then solve for x.  If the graph crosses the y-axis, then that point has an x-coordinate of 0 since all points on the y-axis have x-coordinate 0.  To find the y-intercepts, we set x equal to zero and solve for y.  Thus, if , the y-intercept of the graph is .  Note that we usually just say that  is the y-intercept, rather than more accurately saying that  is the y-intercept.

Example 1

Find the x and y intercepts of the graph of .

Solution1

 The y-intercept is

To find the x-intercept. Substitute 0 for y and solve for x:

 

The y-intercept is at the point (0, -7) and the x-intercept  is ( , 0).

Example 2

Find the x and y intercepts of .

Solution 2

To find the y-intercept, we evaluate .  So, our y-intercept is -2.

To find the x-intercept, we solve

So, our x-intercepts are 1, -2

Example 3

Find the x and y intercepts of

Solution 3

First, we evaluate  to see that the y-intercept is 0.  Then, we solve

           
So, the x-intercepts are -3, 0, 5.

Example 4  

Find the x and y intercepts of

Solution 4

First, we set y equal to zero.

So, our x-intercepts are 2 and -2.

Next, we set x equal to zero.

So, our y-intercepts are 3 and -3.