Question

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

Explanation:

Step1: Recall the definition of roots

The real solutions of \( f(x) = 0 \) are the x - intercepts of the graph of \( y = f(x) \), i.e., the values of \( x \) where the graph intersects the x - axis (\( y = 0 \)).

Step2: Identify the x - intercepts from the graph

Looking at the graph, we can see that the graph touches or crosses the x - axis at \( x=-6 \) (a point where the graph touches the x - axis, which is a repeated root) and at \( x = 0 \) (where the graph crosses the x - axis). So the real solutions of \( f(x)=0 \) are \( x=-6 \) and \( x = 0 \).

Answer:

\( x = -6, x = 0 \)