Question

the graph of y = f(x) is shown below. what are all of the real solutions of f(x) = 0? answer additional solution no solution x =

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 crosses or touches the \( x \)-axis.

Step2: Identify the \( x \)-intercepts

Looking at the graph:

• The graph crosses the \( x \)-axis at \( x = -5 \).
• The graph passes through the origin, so \( x = 0 \) is an intercept.
• The graph touches the \( x \)-axis at \( x = 7 \) (a repeated root, but still a real solution).

Answer:

\( x = -5, 0, 7 \)