The function given is $f(x) = x^2 + 4x + 3$. To determine the interval where the function is decreasing, we need to analyze the behavior of its derivative.

1. Find the derivative of $f(x)$: $f'(x) = \frac{d}{dx}(x^2 + 4x + 3) = 2x + 4$

2. Find the critical point where the derivative is zero: $2x + 4 = 0$ Solving for $x$: $x = -2$

   This critical point, $x = -2$, is where the function changes its behavior (increasing or decreasing).

3. Analyze the sign of the derivative:

   • For $x < -2$, the derivative $f'(x) = 2x + 4$ is negative, which means the function is decreasing.
   • For $x > -2$, the derivative $f'(x) = 2x + 4$ is positive, which means the function is increasing.

Thus, the function is decreasing on the interval $(-\infty, -2)$.

Correct answer: $(-\infty, -2)$

Would you like further details on this, or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you find intervals where a function is increasing?
2. What does it mean when the derivative of a function is zero?
3. How can the second derivative help determine the concavity of a function?
4. What are the critical points of a function, and how are they found?
5. How do you graph a quadratic function using its vertex and intercepts?

Tip: Always check the derivative's sign to determine where a function is increasing or decreasing.