Question

which of the following lists of ordered pairs is a function?
a. (2, 4), (3, 9), (4, 16), (5, 25)
b. (0, 2), (4, 2), (0, -4), (4, -2)
c. (1, 1), (2, 3), (1, 5), (4, 7)
d. (2, 4), (-2, 4), (3, 9), (-2, -4)

Explanation:

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (y - value). So we check each option for repeated x - values with different y - values.

Step2: Analyze Option A

For the ordered pairs \((2,4),(3,9),(4,16),(5,25)\), the x - values are \(2,3,4,5\). Each x - value appears only once, so each input has exactly one output.

Step3: Analyze Option B

For the ordered pairs \((0,2),(4,2),(0, - 4),(4, - 2)\), the x - value \(0\) is paired with \(2\) and \(-4\), and the x - value \(4\) is paired with \(2\) and \(-2\). So there are repeated x - values with different y - values, not a function.

Step4: Analyze Option C

For the ordered pairs \((1,1),(2,3),(1,5),(4,7)\), the x - value \(1\) is paired with \(1\) and \(5\). So there is a repeated x - value with different y - values, not a function.

Step5: Analyze Option D

For the ordered pairs \((2,4),(-2,4),(3,9),(-2,-4)\), the x - value \(-2\) is paired with \(4\) and \(-4\). So there is a repeated x - value with different y - values, not a function.

Answer:

A. \((2, 4),(3, 9),(4, 16),(5, 25)\)