Question

determine whether each relation is a function. then drag the letter corresponding to each function to the function box or the not a function box.
a.

x	y
-5	-2
-3	0
1	3
4	-4

b.
{(0, 5), (2, 7), (5, 13), (6, 7)}
c.
graph of a semi - circle
d.
domain range
-5 -2
-3 -1
0 0
3 2
5 4 6

Explanation:

Step1: Recall function definition

A relation is a function if for each input (x - value) there is exactly one output (y - value).

Step2: Analyze relation A

In relation A, for \(x=-5,y = - 2\); for \(x=-3,y = 0\); for \(x = 1,y=3\); for \(x = 4,y=-4\). Each x - value has a unique y - value. So relation A is a function.

Step3: Analyze relation B

In relation B, the ordered - pairs are \((0,5),(2,7),(5,13),(6,7)\). Each x - value (0, 2, 5, 6) has a unique y - value. So relation B is a function.

Step4: Analyze relation C

For the graph in relation C, using the vertical - line test (if a vertical line intersects the graph at more than one point, it is not a function), a vertical line can intersect the semi - circle at more than one point. So relation C is not a function.

Step5: Analyze relation D

In relation D, the input \(x = 3\) has two outputs \(y = 2\) and \(y = 4\). Since an input has more than one output, relation D is not a function.

Answer:

Function: A, B
Not a Function: C, D