Questions: Indicate whether the function is one-to-one. B=(0,2),(2,-8),(-4,-8) Is the function one-to-one? No Yes

Transcript text: Indicate whether the function is one-to-one. \[ B=\{(0,2),(2,-8),(-4,-8)\} \] Is the function one-to-one? No Yes

Solution

Solution Steps

Step 1: Understand the definition of a one-to-one function

A function is one-to-one if each element in the domain maps to a unique element in the codomain. In other words, no two different inputs can produce the same output.

Step 2: Analyze the given function

The function \( B \) is given as a set of ordered pairs: \[ B = \{(0,2), (2,-8), (-4,-8)\} \] Here, the first element of each pair is the input (domain), and the second element is the output (codomain).

Step 3: Check for repeated outputs

Examine the outputs (second elements) of the ordered pairs:

The output for \( 0 \) is \( 2 \).
The output for \( 2 \) is \( -8 \).
The output for \( -4 \) is \( -8 \).

Notice that both \( 2 \) and \( -4 \) map to the same output \( -8 \). This means the function is not one-to-one because two different inputs produce the same output.

Step 4: Conclusion

Since the function \( B \) has repeated outputs for different inputs, it is not one-to-one. The correct answer is No.