Question

Постройте график функции y=5/x и определите,при каких значениях x она принимает положительные и отрицательные значения? срочно нужно!

Answer 1

Plotting the Function y = 5/x

To plot the function y = 5/x, we can create a graph with x-values ranging from negative infinity to zero and from zero to positive infinity. However, since dividing by zero is undefined, we will exclude the value x = 0 from the graph.

Let's plot the function:

import numpy as np
import matplotlib.pyplot as plt

# Generate x values
x = np.linspace(-10, -0.1, 1000)
x = np.append(x, np.linspace(0.1, 10, 1000))

# Calculate y values
y = 5 / x

# Plot the function
plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = 5/x')
plt.grid(True)
plt.show()

The graph of the function y = 5/x will look like this:


Positive and Negative Values of y

To determine the values of x for which the function y = 5/x takes positive and negative values, we need to consider the sign of y.

1. Positive values of y: The function y = 5/x will take positive values when x is either positive or negative, but not equal to zero. This is because dividing a positive number by a positive number or dividing a negative number by a negative number will result in a positive value. Therefore, the function takes positive values for all x ≠ 0.

2. Negative values of y: The function y = 5/x will take negative values when x is either positive or negative, but not equal to zero. This is because dividing a positive number by a negative number or dividing a negative number by a positive number will result in a negative value. Therefore, the function takes negative values for all x ≠ 0.

In summary: - The function y = 5/x takes positive values for all x ≠ 0. - The function y = 5/x takes negative values for all x ≠ 0.

Please note that the graph and the analysis above are based on the mathematical properties of the function y = 5/x.