This is the last thing I need help with! Please help me to find a solution. Thank You!
f(x) = [ x2 - x - 2 ] / [ x - 3 ]
Divide each term by x: f(x) = [ x2 /x - x / x - 2 / x ] / [ x / x - 3 / x ] = [ x - 1 - 2/x ] / [ 1 - 3/x ]
a) As x --> infinity, this goes to ( x - 1 ) / 1 = x - 1 ---> infinity
b) As x --> - infinity, this goes to - infinity.
c) Since the numerator has a degree one more than the denominator, it has a slant asymptote.
Doing long division, we get a quotient of x + 2
Therefore, the equation of the slant asymptote is: y = x + 2
d) The denominator is x - 3.
Therefore, there will be a vertical asymptote at x = 3.
e) To find the x-intercepts, set y to 0 and solve: 0 = [ x2 - x - 2 ] / [ x - 3 ]
0 = x2 - x - 2
0 = (x - 2)(x + 1)
Therefore, there will be x-intercepts at -1 and 2.
To find the y-intercept, set x to 0 and solve: y = [ 02 - 0 - 2 ] / [ 0 - 3 ]
Therefore, there will be a y-intercept at 2/3.
There are no holes in the graph because there is no factor that is in both the numerator and denominator.
Graphing -- that's up to you ...