Question

the graph of y = f(x) is shown below. what are all of the real solutions of f(x) = 0?

Explanation:

Step1: Understand the problem

We need to find the real solutions of \( f(x) = 0 \), which are the x - intercepts of the graph of \( y = f(x) \) (the points where the graph crosses or touches the x - axis).

Step2: Identify the x - intercepts from the graph

Looking at the graph:

• The graph touches the x - axis at \( x=-4 \) (a repeated root, since it touches the axis and turns around).
• The graph crosses the x - axis at \( x = 0 \) and \( x = 3 \).

Answer:

The real solutions of \( f(x)=0 \) are \( x=-4 \), \( x = 0 \), and \( x = 3 \). So we can write them as \( x=-4,0,3 \) (or list them separately as \( x=-4 \), \( x = 0 \), \( x = 3 \)).