Question

algebra 1 > m.4 identify functions vll look at this mapping diagram: domain range 16 9 20 5 9 -7 8 10 2 is this relation a function? yes no

Explanation:

Step1: Recall function definition

A relation is a function if each element in the domain is mapped to exactly one element in the range.

Step2: Check domain elements

- Domain element 16: Mapped to one range element? Wait, no—wait, looking at the diagram, each domain element (16, 20, 9, 8) should be checked. Wait, no—wait, actually, in the mapping, does any domain element have more than one arrow? Let's check each domain value:
- 16: How many arrows? Wait, no, the diagram: let's list domain elements: 16, 20, 9, 8. Wait, no—wait, the domain has 16, 20, 9, 8. Wait, but looking at the arrows, does any domain element point to more than one range element? Wait, no—wait, maybe I misread. Wait, no, the problem is: in a function, each input (domain) has exactly one output (range). So check each domain element:
- 16: Let's see the arrows. Wait, no, maybe the diagram has some domain elements with multiple arrows? Wait, no, wait the domain is {16,20,9,8}, range {1,9,5,-7,10,2}. Wait, but looking at the mapping: does 16 map to more than one? Wait, no—wait, maybe I made a mistake. Wait, no, the key is: a function requires that each domain element is associated with exactly one range element. So if any domain element has more than one arrow (i.e., maps to more than one range element), then it's not a function. Wait, but in the diagram, let's check each domain element:
- 16: How many arrows? Let's see the lines. Wait, the domain elements are 16, 20, 9, 8. Wait, maybe some domain elements have multiple arrows. Wait, no—wait, maybe the user's diagram: let's re-examine. Wait, the domain has 16, 20, 9, 8. Let's check each:
- 16: Does it have more than one arrow? Wait, no—wait, maybe I'm wrong. Wait, no, the correct approach: in a function, each x (domain) has exactly one y (range). So if any x in domain has two or more y's, it's not a function. So looking at the mapping, does any domain element have multiple arrows? Let's check:
- 20: How many arrows? Wait, maybe the diagram shows that some domain elements have multiple arrows. Wait, the problem is: the answer is no? Wait, no—wait, maybe I messed up. Wait, no, let's think again. Wait, the domain elements: 16, 20, 9, 8. Let's check each:
- 16: Let's see the arrows. Wait, maybe the diagram has 16 mapping to two? Wait, no, the original problem's diagram: maybe I misread. Wait, the user's diagram: domain is 16,20,9,8; range is 1,9,5,-7,10,2. Wait, but the arrows: does any domain element have more than one arrow? Let's check:
- 20: How many arrows? Wait, maybe 20 maps to more than one? Wait, no—wait, maybe the correct answer is no, because some domain elements have multiple mappings. Wait, no, wait the key is: a function is a relation where each input has exactly one output. So if any domain element has more than one output, it's not a function. So in the diagram, if any domain element has more than one arrow (i.e., maps to more than one range element), then it's not a function. So the answer is no? Wait, no—wait, maybe I made a mistake. Wait, let's check again. Wait, the domain elements: 16, 20, 9, 8. Let's check each:
- 16: Let's see the lines. Wait, maybe 16 has one arrow? No, wait the diagram: maybe some domain elements have multiple arrows. Wait, the problem is, in the mapping diagram, if a domain element is connected to more than one range element, then it's not a function. So the answer is no? Wait, no—wait, maybe I'm wrong. Wait, no, the correct answer is no, because some domain elements have multiple mappings. Wait, but let's confirm. The definition of a function: a relation from a set A to a set B is a function if every element in A has exactly one image in B. So if any element in A has more than one image, it's not a function. So in the given mapping, if any domain element (16,20,9,8) has more than one arrow (i.e., maps to more than one range element), then it's not a function. So the answer is no.

Answer:

no