For given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0
In this question, we have been given a function f(x) = x+2/(x + 4) (x + 1)
We need to gaph the given function.
From given function we can observe that the function f(x) is not defined for x = -4 and x = -1
Also, the degree of numerator = 1 and the degree of denominator is 2
We know that if the degree of the denominator > degree of the numerator, then a horizontal asymptote is at y = 0 (x - axis)
The graph of function f(x) is as shown below.
The x-intercept for the graph function f(x) is at (-2, 0)
Also, as x → -∞, f(x)→0
and as x → +∞, f(x)→0
Therefore, for given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0
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