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Math  /  Algebra

Question\begin{tabular}{|c|l|l|l|l|c|c|} \hlinexx & 1 & 2 & 3 & 4 & 5 & 6 \\ f(x)f(x) & 1 & 2 & 4 & 8 & 16 & 32 \\ \hline \end{tabular}
A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. If it is one-to-one, enter " yy " below. If not, enter " nn " below. □\square

Studdy Solution

STEP 1

1. A function f 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) 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) f(a) = f(b) , then a=b 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) f(x) .
The table is: x123456f(x)12481632\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}

STEP 5

Check if any output value is repeated for different input values.
From the table: - f(1)=1 f(1) = 1 - f(2)=2 f(2) = 2 - f(3)=4 f(3) = 4 - f(4)=8 f(4) = 8 - f(5)=16 f(5) = 16 - f(6)=32 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:
y \boxed{y}

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