SOLUTION: Let f(x) = 2x^2+5x-12/2x^2+x-15 1) A y intercept at the point Be sure to put your ordered pair in parentheses. 2) x intercepts at the point(s) Be sure to put your o

Algebra ->  Equations -> SOLUTION: Let f(x) = 2x^2+5x-12/2x^2+x-15 1) A y intercept at the point Be sure to put your ordered pair in parentheses. 2) x intercepts at the point(s) Be sure to put your o      Log On


   

Question 1153073: Let f(x) = 2x^2+5x-12/2x^2+x-15
1) A y intercept at the point

Be sure to put your ordered pair in parentheses.
2) x intercepts at the point(s)

Be sure to put your ordered pair in parentheses.
3) Vertical asymptotes at x =

If there is more than one vertical intercept, separate the x-values with a comma.
4) Horizontal asymptote at y =
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%282x%5E2%2B5x-12%29%2F%282x%5E2%2Bx-15%29...factor
f%28x%29+=+%28%282x-3%29%28x+%2B+4%29%29%2F%28%282x+-+5%29%28x+%2B+3%29%29

1) A y intercept at the point:(0,y)

x=0
f%280%29+=+%28%282%2A0-3%29%280+%2B+4%29%29%2F%28%282%2A0+-+5%29%280+%2B+3%29%29
f%280%29+=+%28%28-3%29%28+4%29%29%2F%28%28-5%29%283%29%29
f%280%29+=+-12%2F-15
f%280%29+=+4%2F3
y intercept at the point:(0,4%2F3)


2) x intercepts at the point(s): (x,0)

set f%28x%29=0
0=+%28%282x-3%29%28x+%2B+4%29%29%2F%28%282x+-+5%29%28x+%2B+3%29%29-> will be equal to zero for all x that make numerator equal to zero
0=+%282x-3%29%28x+%2B+4%29
solutions:
0=+%282x-3%29=>2x=3=>x=3%2F2
0=+%28x+%2B+4%29=>x=-4
x intercepts at the point(s): (3%2F2,0), (-4,0)

3) Vertical asymptotes at x =

for all x that make denominator equal to zero:
=>x=5%2F2
%28x+%2B+3%29=0%7D%7D=%3E%7B%7B%7Bx=-3

vertical intercepts are: x=5%2F2,x=-3
4) Horizontal asymptote at y =
-----------------
lim%28x-%3E-infinity%29+%282+x%5E2+%2B+5+x+-+12%29%2F%282+x%5E2+%2B+x+-+15%29+=+1
lim%28x-%3Einfinity%29+%282+x%5E2+%2B+5+x+-+12%29%2F%282+x%5E2+%2B+x+-+15%29+=+1
Horizontal asymptote at y=1