SOLUTION: My teacher would like us to graph, including any oblique asymptotes, y= f(x) = X^2+5
-----
x+1
find intercepts, verticle asymptotes, and horizontal asymptotes. I have the grap
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Question 112972This question is from textbook college algebra
: My teacher would like us to graph, including any oblique asymptotes, y= f(x) = X^2+5
-----
x+1
find intercepts, verticle asymptotes, and horizontal asymptotes. I have the graph done, I just need to know how to do the written work.
Thank you.
This question is from textbook college algebra
Answer by chitra(359) (Show Source): You can put this solution on YOUR website!
The given expression is: y = f(x) =
The intercepts are given as follows:
Y - intercept put x = 0
==> y = (0 + 5)/(0 + 1)
==> y = 5/1
==> y = 5
The x-intercepts are given when y = 0
==> 0 =
==> 0 =
==> x^2 = - 5
==> (+ -)
The graph looks this way:
The vertical and the horizontal asymptotes are found as follows:
The vertical asymptotes come from the zeroes of the denominator, so I'll set the denominator equal to zero and solve.
x + 1 = 0
==> x = -1
Thus the vertical asymptotes.
Since the degree of the numerator is one greater than the degree of the denominator, I'll have a slant asymptote (not a horizontal one), and I'll find the slant asymptote by long division.
Thus by long dision we find that y = x + 1 is the slant asymptote for the given equation.
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