Question

Построить график функции: у=х^3-4х/х-2 - 2х.

Answer 1

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Answer 2

To plot the function $y = \frac{x^3-4x}{x-2} - 2x$, we'll first need to simplify it before plotting. The given expression can be simplified as follows:

$y = \frac{x^3 - 4x}{x - 2} - 2x$

First, find a common denominator for the first term:

$y = \frac{(x^3 - 4x) - 2x(x - 2)}{x - 2}$

Now, expand the expression in the numerator:

$y = \frac{x^3 - 4x - 2x^2 + 4x}{x - 2}$

Combine like terms in the numerator:

$y = \frac{x^3 - 2x^2}{x - 2}$

The function is now in a simplified form. To plot the graph, we can use any graphing tool or software. Here's how the graph looks like:

As you can see, the graph has a vertical asymptote at $x = 2$ since the denominator becomes zero at that point. The graph also exhibits a cusp-like behavior near $x = 0$.