Question

Построить график функции y=(x+2)^2/(x^2+4)

Answer 1

..................................................................................

Answer 2

Может правильно, а может и неправильно. все возможно

Answer 3

Graph of the Function y=(x+2)^2/(x^2+4)

To graph the function y=(x+2)^2/(x^2+4), we can start by analyzing the behavior of the function at different points.

Let's begin by finding the x-intercepts, y-intercepts, and any vertical asymptotes.

To find the x-intercepts, we set y=0 and solve for x:

(x+2)^2/(x^2+4) = 0

Since the numerator is a perfect square, it can never be equal to zero. Therefore, there are no x-intercepts.

To find the y-intercept, we set x=0:

y = (0+2)^2/(0^2+4) = 4/4 = 1

So the y-intercept is (0, 1).

Now let's analyze the vertical asymptotes. Vertical asymptotes occur when the denominator of the function is equal to zero. In this case, the denominator is x^2+4. However, since the denominator is always positive, there are no vertical asymptotes.

Next, let's find the horizontal asymptotes. To do this, we can analyze the behavior of the function as x approaches positive and negative infinity.

As x approaches positive infinity, both the numerator and denominator of the function approach infinity. Therefore, the function approaches y=1 as x approaches positive infinity.

As x approaches negative infinity, both the numerator and denominator of the function approach infinity. Therefore, the function also approaches y=1 as x approaches negative infinity.

So the horizontal asymptote of the function is y=1.

Now, let's plot some additional points to get a better understanding of the graph.

When x=-2, the function becomes undefined since it results in division by zero. However, we can see that as x approaches -2 from the left or right, the function approaches positive infinity. Therefore, we can say that there is a vertical asymptote at x=-2.

When x=-1, the function evaluates to y=1/2.

When x=-3, the function evaluates to y=9/5.

Based on these points and the information we gathered earlier, we can sketch the graph of the function y=(x+2)^2/(x^2+4).


Please note that the graph is an approximation and may not be perfectly accurate. It is always recommended to use graphing software or a graphing calculator for precise graphs.