Question

The graph of F(X), shown below, has the same shape as the graph of

G(x) = x4 – x2, which contains the point (0,0). Which of the following is the
equation of F(x)?

Answer 1

The correct option is;

D. F(x) = x⁴ - x² + 2

Explanation:

From the graph, we have;

The y-intercept = 2, therefore, when x = 0, y = 2

The graph has no x-intercept, therefore, the unction has complex roots

The possible function is F(x) = x⁴ + x² + 2 and F(x) = 2 - x⁴ - x²

The roots of the function, F(x) = x⁴ - x² + 2, is given as follows;

0 = x⁴ - x² + 2

x = (1 ± √(1 - 8))/(2) = (1 ± √(-7))/(2) which are imaginary roots

For F(x) = 2 - x⁴ - x², we have;

0 = 2 - x⁴ - x²

x = (1 ± √(1 + 8))/(2) = (1 ± 3)/(2)

x = 2 or x = -1, therefore, the function, F(x) = 2 - x⁴ - x², has real roots and the only possible solution is F(x) = x⁴ + x² + 2