Let's go over the tasks step-by-step based on the image you've uploaded:

Task 1:

You are given a function $y = f(x)$ as shown in the graph in Figure 2, and you need to plot the graphs of:

1. $y = -f(x)$: This reflects the graph over the x-axis (invert the y-values).
2. $y = f(-x)$: This reflects the graph over the y-axis (invert the x-values).

Task 2:

You need to plot the following functions:

1. $y = -3x^2$: This is a downward-opening parabola since the coefficient of $x^2$ is negative.
2. $y = \sqrt{5x}$: This is a square root function, starting from $x = 0$.

Task 3:

You are asked to find the vertex coordinates of the following parabolas:

1. $y = x^2 + 7$: The vertex is at $(0, 7)$, since the parabola is of the form $y = x^2 + c$.
2. $y = (x + 8)^2$: The vertex is at $(-8, 0)$, since the form is $(x - h)^2$, and in this case, $h = -8$.
3. $y = (x - 6)^2 + 9$: The vertex is at $(6, 9)$.

Task 4:

You are asked to plot the graph of $y = \sqrt{x}$, and based on that:

1. $y = \sqrt{x - 4}$: This is a horizontal shift of the square root function to the right by 4 units.
2. $y = 3 + \sqrt{x + 1}$: This is a vertical shift up by 3 units and a horizontal shift to the left by 1 unit.

Additionally, you are asked to plot $y = \frac{2x}{x + 3}$, which is a rational function.

Would you like details on how to reflect or shift the graphs, or any specific part explained further?

Here are 5 related questions to expand on these topics:

1. How do we determine the range of the function $y = \sqrt{5x}$?
2. What is the effect of shifting $y = \sqrt{x}$ by 4 units to the left on its domain and range?
3. How would the graph of $y = -f(-x)$ differ from the reflections you did earlier?
4. Can you describe the asymptotic behavior of the rational function $y = \frac{2x}{x + 3}$?
5. How do the transformations affect the domain and range of the function $y = -3x^2$?

Tip: For reflections, it's useful to apply transformations one at a time to avoid mistakes.