Math Snap

STEP 1

1. A function $f$ is one-to-one if each output value corresponds to exactly one input value.
2. The table provides discrete values of the function $f(x)$.

STEP 2

1. Understand the concept of a one-to-one function.
2. Analyze the given table of values.
3. Determine if the function is one-to-one.

STEP 3

A one-to-one function has the property that if $f(a) = f(b)$, then $a = b$. This means no two different inputs should map to the same output.

STEP 4

Examine the provided table of values for $f(x)$.
The table is:
$$\begin{array}{|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\ f(x) & 1 & 2 & 4 & 8 & 16 & 32 \\ \hline \end{array}$$

Check if any output value is repeated for different input values.
From the table:
- $f(1) = 1$
- $f(2) = 2$
- $f(3) = 4$
- $f(4) = 8$
- $f(5) = 16$
- $f(6) = 32$
Each output is unique to its input, indicating that the function is one-to-one.
The function is one-to-one, so the answer is:
$$\boxed{y}$$