SOLUTION: 1. f(x)= x^+3x-4 divide over x^+5x-6 find va vertical asymptote ha horizontal asymptote x-intercept y=intercept and graph it w the t chart plz help me s

Algebra ->  Rational-functions -> SOLUTION: 1. f(x)= x^+3x-4 divide over x^+5x-6 find va vertical asymptote ha horizontal asymptote x-intercept y=intercept and graph it w the t chart plz help me s      Log On


   

Question 39325: 1. f(x)= x^+3x-4 divide over x^+5x-6
find va vertical asymptote
ha horizontal asymptote
x-intercept
y=intercept
and graph it w the t chart plz help me solve this problem thank you
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+%28x%5E2%2B3x-4%29%2F%28x%5E2%2B5x-6%29+
+f%28x%29+=+%28%28x%2B4%29%28x-1%29%29%2F%28%28x%2B6%29%28x-1%29%29+
+f%28x%29+=+%28x%2B4%29%2F%28x%2B6%29+

so, we are to avoid x+6=0, which is when x=-6. This the vertical asymptote.

Now for the horizontal one:
+y+=+%28x%2B4%29%2F%28x%2B6%29+
+y%28x%2B6%29+=+x%2B4+
+xy%2B6y+=+x%2B4+
+xy-x+=+4-6y+
+x%28y-1%29+=+4-6y+
+x+=+%284-6y%29%2F%28y-1%29+

so, we are to avoid y-1=0, which is when y=1. this is the horizontal asymptote.

So, plot the axes and draw the 2 dotted asymptotes. We need a couple of points to anchor the 2 halves of the plot.

So, when x=0, we have y=4/6 --> y=2/3
and when y=0, we have x=4/(-1) --> x=-4

Plot these 2 points and draw a curve in the quadrant joining these points and heading towards the asymptotes. Then draw a matching curve in the diagonally opposite quadrant of your graph.

If you want to, pick some random value of x, say x=-5 and find y. It should be a small-ish negative y-value, since the curve crosses the x-axis at x=-4.

jon.