The function given is:

$f(x) = \sqrt{x + 4}$

Step 1: Determine the Domain

Since this is a square root function, the expression under the square root, $x + 4$, must be non-negative: $x + 4 \geq 0 \Rightarrow x \geq -4$ Thus, the domain of $f(x)$ is $x \geq -4$.

Step 2: Identify Key Points

The problem asks for four points: the leftmost point and three additional points. Let's choose values of $x$ within the domain:

1. Leftmost point: $x = -4$ $f(-4) = \sqrt{-4 + 4} = \sqrt{0} = 0$ So, one point is $(-4, 0)$.

2. Next point: $x = 0$ $f(0) = \sqrt{0 + 4} = \sqrt{4} = 2$ Another point is $(0, 2)$.

3. Next point: $x = 5$ $f(5) = \sqrt{5 + 4} = \sqrt{9} = 3$ This gives the point $(5, 3)$.

4. Next point: $x = 9$ $f(9) = \sqrt{9 + 4} = \sqrt{13} \approx 3.6$ This point is approximately $(9, 3.6)$.

Step 3: Plot the Points

On the graph, plot these points:

• $(-4, 0)$
• $(0, 2)$
• $(5, 3)$
• $(9, 3.6)$

These points represent the curve of $f(x) = \sqrt{x + 4}$. The function will start at $(-4, 0)$ and increase gradually to the right as $x$ increases.

Would you like more details on graphing techniques or the function's behavior?

Additional Questions for Further Exploration:

1. How would the graph change if the function were $f(x) = \sqrt{x - 4}$?
2. What is the range of the function $f(x) = \sqrt{x + 4}$?
3. How would you determine the inverse of $f(x) = \sqrt{x + 4}$?
4. How do transformations affect the graph of a square root function?
5. How can you use this function to model real-world situations?

Tip:

When working with square root functions, always check the domain since square roots are only defined for non-negative values inside the radical.