To determine if the relation shown in the table is a function, we need to look at the x-values (inputs) and their corresponding f(x) values (outputs).
A relation is classified as a function if each input (x-value) is associated with exactly one output (f(x) value). In other words, no x-value can map to more than one f(x) value.
Let's examine the x-values from the table:
- For \( x = 3 \), \( f(3) = 2 \)
- For \( x = 0 \), \( f(0) = 1 \)
- For \( x = 5 \), \( f(5) = -7 \)
- For \( x = -3 \), \( f(-3) = 2 \)
In this table, the x-values are 3, 0, 5, and -3. Each of these x-values is unique and corresponds to exactly one f(x) value:
- \( 3 \) maps to \( 2 \)
- \( 0 \) maps to \( 1 \)
- \( 5 \) maps to \( -7 \)
- \( -3 \) maps to \( 2 \)
Since no x-value is repeated, and each one maps to only one unique f(x) value, we can conclude that this relation is indeed a function.
Conclusion: Yes, the relation is a function because each x-value has a unique corresponding f(x) value.