We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
159
1
avatar+166 

The graph of \(y = \frac{p(x)}{q(x)}\) is shown below, where \(p(x)\) is linear and \(q(x)\) is quadratic. (Assume that the grid lines are at integers.)



Find \(\frac{p(-1)}{q(-1)}.\)

 Jul 12, 2019
 #1
avatar+105195 
+1

Since  x = -3  and  x = 2   are vertical asymptotes, then we might guess that the denominator might be of the form...

a(x + 3) (x - 2)

 

Since  (0,0)  is on the graph, then the numerator must be of the form.... bx

 

And the points  (3,1)  and (-2, 1)   are on the graph

 

So...we have that

 

        b (3)                                  3b 

____________   =    1    ⇒    ________ =    1   ⇒   3b  = 6a  ⇒  b = 2a

a (3 + 3)(3 - 2 )                          6a

 

And

 

     b(-2)                                        -2b

______________  =     1   ⇒     ________  =  1  ⇒   -2b = -4a   ⇒  -2(2a)  = -4a ⇒ a  = 1 

a(-2 + 3) (-2 - 2)                         a(1)(-4)

 

 

So  p   = bx =    2(a)x  =  2(1)x  =   2x

 

And q  =  1 (x + 3) (x - 2)  =  (x + 3) (x - 2)

 

So  p(-1 )               2(-1)                       -2                   -1            1

      ____   =     ____________   =   ________  =     ___  =     ___

      q (-1)         (-1 + 3) (-1 - 2)           (2) (-3)              -3            3

 

 

cool cool cool

 Jul 13, 2019

29 Online Users

avatar
avatar