Question

Y=x²-2,x≥0,найти D(y),E(y) график​

Answer 1

D(y): x€[0; +∞)

E(y):

y min = y(0) = -2

y€[-2; +∞)

Answer 2

To find the domain and range of the function $y = x^2 - 2$ given that $x \geq 0$, we can proceed as follows:

1. Domain (D(y)): The domain of a function represents the set of all possible input values (x-values) for which the function is defined. Since the given condition is $x \geq 0$, the domain of the function $y = x^2 - 2$ is all non-negative real numbers: $D(y) = \{x \in \mathbb{R} \mid x \geq 0\}$

2. Range (E(y)): The range of a function represents the set of all possible output values (y-values) that the function can take on. To find the range, we can analyze the behavior of the function.

As $x$ approaches positive infinity, $x^2$ grows without bound, and as $x$ gets closer to zero, $x^2$ still remains positive. So, the lowest value that $x^2$ can take is 0 (when $x = 0$). When we subtract 2 from $x^2$, the lowest value of $y$ becomes -2.

Therefore, the range of the function is all real numbers greater than or equal to -2: $E(y) = \{y \in \mathbb{R} \mid y \geq -2\}$

Now, let's plot the graph of the function $y = x^2 - 2$ for $x \geq 0$:

To plot the graph, we'll consider some key points and the behavior of the function:

1. When $x = 0$, $y = 0^2 - 2 = -2$, so the graph passes through the point (0, -2).
2. When $x = 1$, $y = 1^2 - 2 = -1$, so the graph passes through the point (1, -1).
3. As $x$ gets larger, $y = x^2 - 2$ becomes arbitrarily large (but always greater than or equal to -2).

Now, let's plot the graph:

(Note: The graph will only be plotted for $x \geq 0$ since the given function is defined only for non-negative values of $x$.)

luaCopy code
      ^
      |
  3 --|       *
  2 --|        \
  1 --|         *   
  0 --|_____*____*____*____*____*____>
      0   1    2    3    4    5   x

Please note that the graph is a parabola that opens upward and is shifted downward by 2 units. It touches the x-axis at the point (0, -2) and continues upward indefinitely, but it never crosses the x-axis again since $x \geq 0$.