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X and Y Intercepts

X-INTERCEPTS:  Where the graph crosses the x-axis.

Hey, this is the same as finding the zeros!

Set  

f ( x ) = 0

   and solve

But, here's the cool thing:
For these rational guys, you just need to set the numerator = 0 and solve!

Why?  That's a great question -- I'm glad you asked...

Well, when a fraction is 0, it's the same as saying the numerator is 0:

0 / 3 = 0

So, set the numerator = 0 and solve.

Check it out:

f ( x ) = ( x^2 - x - 6 ) / ( x^2 - 1 )

numerator = 0 gives x^2 - x - 6 = 0 which gives ( x - 3 ) ( x + 2 ) = 0 which gives x - 3 = 0 or x + 2 = 0 which gives x = 3 and x = -2

So, the x-intercepts are the points

( -2 , 0 ) and ( 3 , 0 )

YOUR TURN:

Find the x-intercepts of   f ( x ) = ( x - 3 ) / ( x^2 - 3x - 10 )

BIG NOTE:

These processes find the ONLY intercepts!
There will NOT be any others!!

(This info will be very important.)