a. See image of the graph attached below.
b. The relation is a function
c. The domain is: {-1, 0, 1, 2, 3, 4, 5, 6, 7}
Range is: {-4, -3, 0, 5, 12}
How to Determine if a Relation is a Function?
If every x-value in a relation has exactly one y-value that corresponds to it, then the relation is a function.
A graph that has a U-shape with a minimum, that is the pointed U-shape is downwards, it means the relation has x-values that have exactly one y-value that corresponds to to it, therefore, the relation is a function.
a. To fill out the table, plug in the value of x into y = x² - 6x + 5:
When x = -1:
y = (-1)² - 6(-1) + 5 = 12
When x = 0:
y = (0)² - 6(0) + 5 = 5
When x = 1:
y = (1)² - 6(1) + 5 = 0
When x = 2:
y = (2)² - 6(2) + 5 = -3
When x = 3:
y = (3)² - 6(3) + 5 = -4
When x = 4:
y = (4)² - 6(4) + 5 = -3
When x = 5:
y = (5)² - 6(5) + 5 = 0
When x = 6:
y = (6)² - 6(6) + 5 = 5
When x = 7:
y = (7)² - 6(7) + 5 = 12
Thus, the graph has a minimum of -4.
b. The relation is a function because each x-value has exactly one y-value related to it.
c. The domain is: {-1, 0, 1, 2, 3, 4, 5, 6, 7}
Range is: {-4, -3, 0, 5, 12}
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