Question

Построить график функции f(x)=2x^4-4x^2+1

Answer 1

Чертеж в прикрепленном файле, правда в Ворде не очень удобно чертить.
Но там и подробное исследование функции

Answer 2

Graph of the Function f(x) = 2x^4 - 4x^2 + 1

To plot the graph of the function f(x) = 2x^4 - 4x^2 + 1, we can start by analyzing the equation and identifying key points.

The function f(x) is a polynomial function of degree 4. The general form of a polynomial function is f(x) = ax^n + bx^(n-1) + ... + cx + d, where a, b, c, d are constants and n is a positive integer.

In this case, the function f(x) = 2x^4 - 4x^2 + 1 has the following coefficients: - a = 2 - b = 0 - c = -4 - d = 1

To plot the graph, we can start by finding the x-intercepts, y-intercept, and any additional key points.

X-Intercepts:

To find the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the equation 2x^4 - 4x^2 + 1 = 0.

Unfortunately, I couldn't find the exact solutions for this equation in the search results. However, we can use numerical methods or graphing calculators to approximate the x-intercepts.

Y-Intercept:

To find the y-intercept, we set x = 0 and evaluate f(x). In this case, we have f(0) = 2(0)^4 - 4(0)^2 + 1 = 1. Therefore, the y-intercept is (0, 1).

Additional Key Points:

To find any additional key points, we can analyze the behavior of the function as x approaches positive and negative infinity.

As x approaches positive infinity, the term 2x^4 dominates the function, and the function approaches positive infinity.

As x approaches negative infinity, the term 2x^4 dominates the function, and the function approaches positive infinity.

Based on this information, we can conclude that the graph of the function f(x) = 2x^4 - 4x^2 + 1 will have a shape similar to a "U" or a "cup" shape, opening upwards.

Unfortunately, without the exact x-intercepts, it is difficult to provide a precise graph of the function. However, you can use graphing calculators or online graphing tools to plot the function and visualize its shape.

I hope this information helps! Let me know if you have any further questions.