Question

Функция y=-√x. Её график и свойства

Answer 1

Вот график этой ф-ции)

Answer 2

Function y = -√x

The function y = -√x represents a downward-facing square root function. It is a simple mathematical function that relates the input value x to the output value y. The negative sign in front of the square root indicates that the graph of the function is reflected across the x-axis.

Graph of the Function

To visualize the graph of the function y = -√x, we can plot it on a coordinate plane. Since the square root function is only defined for non-negative values of x, the graph will only exist in the domain where x ≥ 0.

The graph of y = -√x starts at the point (0, 0) and extends to the left along the x-axis. As x increases, the value of y decreases, resulting in a downward-sloping curve. The graph approaches the x-axis but never touches or crosses it.

Properties of the Function

1. Domain: The function y = -√x is defined for all non-negative real numbers, i.e., x ≥ 0. 2. Range: The range of the function is all real numbers less than or equal to zero, i.e., y ≤ 0. 3. Symmetry: The graph of y = -√x is symmetric with respect to the y-axis. This means that if we reflect any point (x, y) on the graph across the y-axis, we will get the corresponding point (-x, y). 4. Intercepts: The function does not intersect the x-axis since the square root of a non-negative number is always positive or zero. The y-intercept is (0, 0). 5. Asymptote: The graph of y = -√x approaches the x-axis as x approaches positive infinity. This means that the x-axis acts as a horizontal asymptote for the function.

Example

Let's consider an example to better understand the properties of the function. If we evaluate the function y = -√x at x = 4, we get:

y = -√4 = -2

So, when x = 4, y = -2. This point (-2, 4) lies on the graph of the function.

Conclusion

In summary, the function y = -√x represents a downward-facing square root function. Its graph starts at the point (0, 0) and extends to the left along the x-axis. The function is defined for non-negative values of x and has a range of all real numbers less than or equal to zero. The graph is symmetric with respect to the y-axis and approaches the x-axis as x approaches positive infinity.