Question

relation 1
domain range
r → 6
k → 9
h → - 9
u → - 9
function
not a function
relation 2
domain range
d → d
a → x
u → a
x → u
function
not a function
relation 3
domain range
h star
e star
f star
function
not a function
relation 4
domain range
9 - 3
9 - 8

• 9 - 6
• 9 - 7
• 9 - 9

Explanation:

Step1: Recall function definition

A function is a relation where each element in the domain is paired with exactly one element in the range.

Step2: Analyze Relation 1

Each element in the domain ($r$, $k$, $h$, $u$) has a single - unique output in the range (6, 9, - 9 respectively), so it's a function.

Step3: Analyze Relation 2

The element $u$ in the domain is paired with two different elements ($a$ and $g$) in the range, so it's not a function.

Step4: Analyze Relation 3

Each element in the domain ($h$, $e$, $f$) is paired with only one element (star) in the range. Multiple domain elements can map to the same range element and it's still a function.

Step5: Analyze Relation 4

The element 9 in the domain is paired with - 3 and - 8, and the element - 9 in the domain is paired with - 6, - 7 and - 9. Since some domain elements have multiple range - values, it's not a function.

Answer:

• Relation 1: Function
• Relation 2: Not a function
• Relation 3: Function
• Relation 4: Not a function