Question

постройте график функции F(x)=1-x,если x≥1,x^2-1,если x<1.

Answer 1

Первый - простая прямая, строится по двум точкам, график правее х=1 включительно.

Второй - парабола смещенная по оси у на единицу вниз. График левее х=1, не включая, точка выколота.

Answer 2

Graph of the Function F(x) = 1 - x, if x ≥ 1, and F(x) = x^2 - 1, if x < 1

To graph the function F(x) = 1 - x, if x ≥ 1, and F(x) = x^2 - 1, if x < 1, we can plot two separate functions for the two different conditions.

For x ≥ 1, the function is F(x) = 1 - x. This is a linear function with a slope of -1 and a y-intercept of 1. The graph will be a straight line that starts at (1, 0) and slopes downward to the left.

For x < 1, the function is F(x) = x^2 - 1. This is a quadratic function that opens upward. The graph will be a curve that starts at (-∞, -1), reaches a minimum point at (1, -1), and then continues upward.

Let's plot these two functions on a graph:

import matplotlib.pyplot as plt
import numpy as np

x1 = np.linspace(1, 10, 100)  # x values for x ≥ 1
y1 = 1 - x1  # y values for x ≥ 1

x2 = np.linspace(-10, 1, 100)  # x values for x < 1
y2 = x2**2 - 1  # y values for x < 1

plt.plot(x1, y1, label='F(x) = 1 - x, if x ≥ 1')
plt.plot(x2, y2, label='F(x) = x^2 - 1, if x < 1')

plt.xlabel('x')
plt.ylabel('F(x)')
plt.title('Graph of F(x) = 1 - x, if x ≥ 1, and F(x) = x^2 - 1, if x < 1')
plt.legend()

plt.show()

The resulting graph will show a straight line for x ≥ 1 and a curve for x < 1. The two parts of the graph will meet at the point (1, 0), where the two functions are equal.

Note: The code provided above is a Python code snippet that uses the matplotlib library to plot the graph. You can run this code in a Python environment to visualize the graph.