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 \( f(x) = 0 \). Geometrically, this means finding 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 (where \( y = 0 \)).

Step2: Identify the \( x \)-intercepts from the graph

Looking at the graph:

• The leftmost \( x \)-intercept is at \( x = -3 \) (since the graph crosses the \( x \)-axis here).
• Then, there's an intercept at \( x = 1 \) (the graph crosses the \( x \)-axis here).
• Next, at \( x = 4 \) (the graph crosses the \( x \)-axis here).
• Finally, at \( x = 7 \) (the graph crosses the \( x \)-axis here).

Answer:

The real solutions of \( f(x) = 0 \) are \( x = -3 \), \( x = 1 \), \( x = 4 \), and \( x = 7 \).