Let's analyze the graph and answer the questions given.

1. Type of Point and Value at $x$:

   • The graph has a maximum point, as the function reaches its highest value and then decreases on either side.
   • This occurs at $x = -3$, where the peak of the parabola is located.
   • Thus, the answer is: "The function has a maximum of $3$ at $x = -3$."

2. Increasing Interval:

   • A function is increasing when moving from left to right, the function values rise.
   • In this graph, the function increases from the leftmost point until $x = -3$.
   • Therefore, the interval where the function is increasing is: $(-\infty, -3)$.

3. Decreasing Interval:

   • A function is decreasing when moving from left to right, the function values drop.
   • The graph starts decreasing right after $x = -3$ and continues to decrease as $x$ increases.
   • Hence, the interval where the function is decreasing is: $(-3, \infty)$.

Summary:

• Maximum at $x = -3$ with a value of $3$.
• Increasing on the interval $(-\infty, -3)$.
• Decreasing on the interval $(-3, \infty)$.

Would you like more details or have any questions about this analysis?

Related Questions:

1. How do you find the derivative of a function to determine increasing and decreasing intervals?
2. What is the difference between local maxima and global maxima?
3. How can you find the vertex of a parabola from its equation?
4. What role does the derivative play in finding the concavity of a function?
5. How do you determine if a function has a minimum or maximum without graphing it?

Tip:

Remember, a function is increasing where its derivative is positive, and decreasing where its derivative is negative!