Describe the vertical asymptote(s) and hole(s) for the graph of
y = (x + 2)(x + 4)
_______________
(x + 4)(x + 1)

Question

Describe the vertical asymptote(s) and hole(s) for the graph of 
y = (x + 2)(x + 4)
     _______________
      (x + 4)(x + 1)

angelwings996 · Answer

a.  asymptotes: x = -1 and hole: x = 4
b.  asymptotes: x = 2 and hole: x = -1
c.  asymptotes: x = -1 and hole: x = -4
d.  asymptotes: x = 1 and hole: x = 4

mathstudent55 · Answer

Notice that the (x + 4) in the numerator and the (x + 4) in the denominator cancel out. That means that this function has a graph just like y = (x + 2)/(x + 1). This has an asymptote at x = -1.
What does the (x + 4) in the numerator and denominator do? It creates a hole at
x = -4. Other than that, this is exactly like y = (x + 2)/(x + 1)

angelwings996 · Answer

Okay thanks(: Do you think you could help me with one more ? @mathstudent55

mathstudent55 · Answer

The 5 vs 1 in the numerator causes the shape of teh hyperbola to become flatter.

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