Question
In which choice is \( y \) a function of \( x \) ? A \( (0,3),(3,1),(1,3),(3,8) \) B \( (2,9),(5,6),(8,3),(10,1) \) C \( (4,7),(8,2),(4,0),(0,3) \) D \( (6,6),(7,7),(8,8),(6,8) \)
Ask by Martinez Brooks. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Option B is the only choice where each x-value has a unique y-value, making y a function of x.
Solution
To determine if y is a function of x, we must ensure that each x-value appears only once with one corresponding y-value.
Option A: The ordered pairs are (0,3), (3,1), (1,3), (3,8). Here, x = 3 appears twice (with y = 1 and y = 8), so it is not a function.
Option B: The ordered pairs are (2,9), (5,6), (8,3), (10,1). Each x-value (2, 5, 8, 10) is unique, so y is a function of x.
Option C: The ordered pairs are (4,7), (8,2), (4,0), (0,3). Here, x = 4 appears twice (with y = 7 and y = 0), so it is not a function.
Option D: The ordered pairs are (6,6), (7,7), (8,8), (6,8). Here, x = 6 appears twice (with y = 6 and y = 8), so it is not a function.
Therefore, only Option B represents y as a function of x.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
In order for \( y \) to be a function of \( x \), each input \( x \) must correspond to exactly one output \( y \). Looking at the choices: - In choice A, the input \( 3 \) corresponds to two different \( y \) values (1 and 8), so this does not represent a function. - In choice B, all \( x \) values (2, 5, 8, 10) are unique, corresponding to unique \( y \) values (9, 6, 3, 1). This is a function. - Choice C has the input \( 4 \) corresponding to two different \( y \) values (7 and 0), so it is not a function. - In choice D, the input \( 6 \) corresponds to two different \( y \) values (6 and 8), thus it is not a function either. So, the answer is B!
