Question

the graph of f(x) = x³ - 7x - 6 is shown. based on the graph, what are all of the solutions to f(x) = x³ - 7x - 6? \bigcirc x = -6 \bigcirc x = -2, -1 \bigcirc x = -2, -1, 3 \bigcirc x = -6, -2, -1, 3

Explanation:

Step1: Recall solution definition

Solutions to \( f(x) = x^3 - 7x - 6 \) are the x - intercepts (where \( y = 0 \)) of the graph of \( y = f(x) \).

Step2: Identify x - intercepts

From the graph, we look for the points where the graph crosses the x - axis. The x - coordinates of these points are the solutions. By observing the graph, the graph crosses the x - axis at \( x=-2 \), \( x = -1 \) and \( x=3 \).

Answer:

\( x = -2, -1, 3 \) (the third option: \( x = -2, -1, 3 \))