Question

I dont understand this problem:
Write an equation for a rational function with:

Vertical asymptotes at x = -3 and x = -6

x intercepts at x = 3 and x = 4

y intercept at 3

My answer was: (3(x-3)(x-4))/((x+3)(x+6))

but the answer is: (4.5(x-3)(x-4))/((x+3)(x+6))

Answer 1

vertical asmptotes at -3 and -6 means your denominator has to look like
\[(x+3)(x+6)\]

Answer 2

oh good you got that

Answer 3

yeah, the part I dont understand is the y intercept.

Answer 4

got the x intercept right too

Answer 5

now you have to make sure that when x = 0, y = 3 so replace x by 0 in this
\[\frac{a(x-3)(x-4)}{(x+3)(x+6)}\] set = 0 and solve for a

Answer 6

i get
\[\frac{a(0-3)(0-4)}{(0+3)(0+6)}=3\]

Answer 7

\[a\times \frac{12}{18}=3\]
\[a=3\times \frac{3}{2}\]
\[a=\frac{9}{2}=4.5\]

Answer 8

i meant set = 3, not set = 0 sorry

Answer 9

gotcha, thank you