Select the correct answer.
Which of these tables represents a function?
W.
X.
Y.
Z.
A. W
B. $x$
C. $Y$
D. z
Answer (1)
A function requires each x-value to have only one y-value. Table W is the only table where each x-value has a unique y-value. Therefore, Table W represents a function. A
Explanation
Understanding Functions A function is a relation where each input (x-value) has only one output (y-value). We need to check each table to see if any x-value is associated with more than one y-value.
Analyzing Table W In Table W, the x-values are -1, -2, 0, and 4. The corresponding y-values are 15, 6, 15, and 6. Each x-value has a unique y-value. Therefore, Table W represents a function.
Analyzing Table X In Table X, the x-values are 0, 6, 0, and -2. The corresponding y-values are 4, 15, 6, and -1. The x-value 0 has two different y-values (4 and 6). Therefore, Table X does not represent a function.
Analyzing Table Y In Table Y, the x-values are 4, -1, 6, and 6. The corresponding y-values are 0, -2, -2, and 15. The x-value 6 has two different y-values (-2 and 15). Therefore, Table Y does not represent a function.
Analyzing Table Z In Table Z, the x-values are 6, 4, 15, and 4. The corresponding y-values are -2, 0, -1, and 3. The x-value 4 has two different y-values (0 and 3). Therefore, Table Z does not represent a function.
Conclusion Only Table W represents a function because each x-value has only one corresponding y-value.
Examples
Functions are essential in understanding relationships between variables. For example, the distance traveled by a car is a function of time if the car moves at a constant speed. If the speed changes, the relationship becomes more complex, but it's still a function as long as each moment in time corresponds to a unique distance. Understanding functions helps us model and predict real-world phenomena.
