We are given the following information about the function $f$:

• $f(2) = -4$ (which means the point $(2, -4)$ is on the graph)
• $f(5) = 3.4$ (which means the point $(5, 3.4)$ is on the graph)

Now, let's evaluate the options:

1. $(-4, 2)$: This point is not correct because it reverses the coordinates. The correct point should be $(2, -4)$.
2. $(2, -4)$: This point is correct because $f(2) = -4$.
3. $(3.4, 5)$: This point is not correct because the first coordinate should be 5, not 3.4.
4. $(5, 3.4)$: This point is correct because $f(5) = 3.4$.
5. $(2, 5)$: This point is not correct because the second coordinate should be -4, not 5.

Correct answers:

• $(2, -4)$
• $(5, 3.4)$

Would you like any more details on this? Feel free to ask.

Related questions:

1. What is the difference between a point on a graph and a coordinate pair?
2. How do you interpret function values in terms of graphing?
3. How would you find additional points on the graph of a function if given other values?
4. Can a point with reversed coordinates still be on the graph of a function?
5. What is the significance of a function's notation, such as $f(x)$?

Tip: When you’re given $f(a) = b$, the point $(a, b)$ always lies on the graph of the function.