Question

Исследуйте функцию и постройте ее графикf(x)=x+x^3​

Answer 1

y=x+x·3

y=x+3x

y=4x

4x=0

x=0

Answer 2

Function Analysis and Graph Plotting: f(x) = x + x^3

To analyze the function f(x) = x + x^3 and plot its graph, let's break down the steps:

1. Function Analysis: - The given function is f(x) = x + x^3. - It is a polynomial function of degree 3. - The function has two terms: x and x^3. - The coefficient of x^3 is 1, indicating that the leading term has a positive coefficient. - The function is defined for all real values of x.

2. Graph Plotting: To plot the graph of f(x) = x + x^3, we can follow these steps: - Determine the x and y-axis ranges based on the desired domain and range. - Choose a set of x-values within the chosen domain. - Calculate the corresponding y-values using the function f(x) = x + x^3. - Plot the points (x, f(x)) on the graph. - Connect the plotted points to form a smooth curve.

Let's plot the graph of f(x) = x + x^3:

| x | f(x) = x + x^3 | |----|----------------| | -3 | -18 | | -2 | -10 | | -1 | -2 | | 0 | 0 | | 1 | 2 | | 2 | 10 | | 3 | 18 |

Now, let's plot these points on the graph:


The graph of f(x) = x + x^3 is a cubic function that passes through the points (-3, -18), (-2, -10), (-1, -2), (0, 0), (1, 2), (2, 10), and (3, 18). It has a single inflection point at x = 0 and is symmetric about the y-axis.

Please note that the graph provided above is for illustrative purposes only and may not accurately represent the actual graph of the function. It is recommended to use graphing software or calculators to obtain a more precise graph.