The problem requires identifying the solution set where $f(x) < g(x) < h(x)$. Based on the graph:

1. Step 1: Analyze the intersections of $f(x)$, $g(x)$, and $h(x)$:

   • $f(x)$: A linear function with a negative slope (red line).
   • $g(x)$: A linear function with a positive slope (green line).
   • $h(x)$: A quadratic function opening upwards (blue curve).

2. Step 2: Determine the regions where $g(x) > f(x)$:

   • Identify where the green line ($g(x)$) is above the red line ($f(x)$).
   • This occurs for $x > -4$ (where $g(x)$ and $f(x)$ intersect).

3. Step 3: Determine the regions where $h(x) > g(x)$:

   • Identify where the blue curve ($h(x)$) is above the green line ($g(x)$).
   • This occurs for $x > 0$ (where $g(x)$ and $h(x)$ intersect).

4. Step 4: Combine conditions for $f(x) < g(x) < h(x)$:

   • All three conditions are satisfied when $x > 0$.

Solution:

The solution set is: $x \in (0, \infty)$

Would you like me to explain further or assist with similar problems?

Related Questions:

1. How do you find the points of intersection between functions algebraically?
2. Can you explain how to determine inequalities involving three functions graphically?
3. What are the key steps to graph and compare quadratic and linear functions?
4. How does the shape of the quadratic function influence its relation to linear functions?
5. What real-life scenarios require solving inequalities between multiple functions?

Tip:

When comparing multiple functions graphically, always carefully analyze intersections and their corresponding $x$-values to define solution sets accurately.