Identify the Function's Graph Passing Through Point (2,8)

To solve this problem, we will check which of the given functions passes through the point $(2, 8)$ by substituting $x = 2$ and verifying if the resulting $y$-value is 8.

• Check each function:
• 1. For $y = \frac{x}{4}$:

Substitute $x = 2$:
$y = \frac{2}{4} = \frac{1}{2}$
This does not satisfy the condition $y = 8$.

• 2. For $y = 4x$:

Substitute $x = 2$:
$y = 4 \times 2 = 8$
This satisfies the condition $y = 8$.

• 3. For $y = -4x$:

Substitute $x = 2$:
$y = -4 \times 2 = -8$
This does not satisfy the condition $y = 8$.

• 4. For $y = x^4$:

Substitute $x = 2$:
$y = 2^4 = 16$
This does not satisfy the condition $y = 8$.

Therefore, the only function that passes through the point $(2, 8)$ is $y = 4x$.

Thus, the solution to the problem is $y = 4x$.