Answer:
The function rule is
[tex]f: x\to \: {x}^{2} - 1[/tex]
Step-by-step explanation:
The given ordered pairs are (0,-1), (1,0),(2,3),(3,8),(4,15)
We can observe the following pattern.
[tex]f(0) = {0}^{2} - 1 = - 1[/tex]
[tex]f(1) = {1}^{2} - 1 = 0[/tex]
[tex]f(2) = {2}^{2} - 1 = 3[/tex]
[tex]f(3) = {3}^{2} - 1 = 8[/tex]
[tex]f(4) = {4}^{2} - 1 = 15[/tex]
When we generalize this pattern, we obtain:
[tex]f(x) = {x}^{2} - 1[/tex]
This is the function equation.
The function rule is
[tex]f: x\to \: {x}^{2} - 1[/tex]
