Let's analyze each part of the question based on the graph to help you get the correct answers:

1. Part (a): Intervals where $f$ is increasing

   • To determine where $f$ is increasing, look for segments where the curve is moving upward as $x$ increases.
   • Based on the graph, $f$ appears to be increasing over the intervals $(0, 1)$ and $(4, 7)$, which you entered correctly.

2. Part (b): Intervals where $f$ is decreasing

   • Here, you need intervals where the curve moves downward as $x$ increases.
   • The graph shows a downward slope between $x = 1$ and $x = 3$. This answer, $(1, 3)$, is correct as indicated by the green checkmark.

3. Part (c): Intervals where $f$ is concave upward

   • The function is concave upward where it curves in an upward "U" shape.
   • The graph suggests that the curve is concave upward approximately between $(3, 5)$.

4. Part (d): Intervals where $f$ is concave downward

   • The function is concave downward where it has a "n" or downward curve shape.
   • Observing the graph, the concave downward intervals appear to be approximately $(0, 3)$ and $(5, 7)$.

5. Part (e): Points of inflection

   • Points of inflection occur where the concavity changes, so look for points around $x = 3$ and $x = 5$.
   • Based on this graph, the inflection points appear to be near $(3, y)$ and $(5, y)$.