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Rational Functions - 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
 
x^2 - x - 6 ... ( x - 3 )( x + 2 ) = 0 ... x - 3 = 0 or x + 2 = 0 ... x = 3 , x = -2
 
 

So, the x-intercepts are the points

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

 

TRY IT:

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.)