The question is asking which point lies on the graph of the function $f(x) = 4^x$.

To determine which point is on the graph, let's check the values of $f(x) = 4^x$ for the $x$-values in the given options:

1. Option A: (0, 0) $f(0) = 4^0 = 1 \quad \text{(not equal to 0)}$ So, $(0, 0)$ is not on the graph.

2. Option B: (0, 4) $f(0) = 4^0 = 1 \quad \text{(not equal to 4)}$ So, $(0, 4)$ is not on the graph.

3. Option C: (1, 4) $f(1) = 4^1 = 4$ This matches the point $(1, 4)$. So, this point is on the graph.

4. Option D: (4, 1) $f(4) = 4^4 = 256 \quad \text{(not equal to 1)}$ So, $(4, 1)$ is not on the graph.

The correct answer is Option C: (1, 4).

Would you like any further explanation or details on this?

5 Related Questions:

1. How do you graph exponential functions like $f(x) = 4^x$?
2. What are the key characteristics of an exponential growth function?
3. How can we determine the domain and range of $f(x) = 4^x$?
4. How does changing the base in an exponential function affect its graph?
5. How can we solve for $x$ in equations of the form $4^x = y$?

Tip:

In exponential functions of the form $f(x) = a^x$, as $x$ increases, the function grows rapidly for $a > 1$, and the graph has a horizontal asymptote at $y = 0$.