Question

how many real solutions does the equation $y = -x^3 - x^2 + 5x + 2$ have? (1 point) real solutions

Explanation:

Step1: Understand the problem

We need to find the number of real solutions of the equation \( y = -x^3 - x^2 + 5x + 2 \). The real solutions of the equation \( y = f(x) \) are the x - intercepts of the graph of \( y = f(x) \), i.e., the points where the graph intersects the x - axis (where \( y = 0 \)).

Step2: Analyze the graph

Looking at the given graph of the function \( y=-x^{3}-x^{2}+5x + 2\), we observe the number of times the graph intersects the x - axis. From the graph, we can see that the curve intersects the x - axis at three points.

Answer:

3