Question

for each relation, decide whether it is a function or not.
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 -> g
x -> u
function
not a function
relation 3
domain range
h star
e star
f star
function
relation 4
domain range
9 - 3
9 - 8

• 9 - 6
• 9 - 7

Explanation:

Step1: Recall function definition

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

Step2: Analyze Relation 1

Each element in the domain ($r$, $k$, $h$, $u$) is paired with a single element in the range ($6$, $9$, $- 9$). So it is 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 is not a function.

Step4: Analyze Relation 3

Each element in the domain ($h$, $e$, $f$) is paired with the same element "star" in the range, but still each domain - element has a unique pairing. So it is a function.

Step5: Analyze Relation 4

The element $9$ in the domain is paired with two different elements ($-3$ and $-8$), and the element $-9$ in the domain is paired with two different elements ($-6$ and $-7$). So it is not a function.

Answer:

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