Answer:
The rule that represents the function is [tex]y=x^2+1[/tex] therefore the function is [tex]f(x)=x^2+1[/tex]
Step-by-step explanation:
We have 5 ordered pairs in the plane xy. This means that every pair has the form (x, y).
Then, we have 5 values of x, which will give us 5 values of y, using the rule that represents the function.
The easy evaluation is that when x=0, the value of y is y=1, and then we can evaluate the rule for x=-1, and x=1, the value of y is the same, y=2. We can see here that we have a parabolic function, that is not centered in the origin of coordinates because when x=0, y=1.
So we propose the rule [tex]y=x^2+1[/tex] which is correct for the first 3 values of x.
Now, we evaluate the proposed rule when x=2, and when x=3. This evaluations can be written as
[tex]f(2)=2^2+1=5[/tex]
[tex]f(3)=3^2+1=10[/tex]
Therefore, the rule is correct, and the function is
[tex]f(x)=x^2+1[/tex]
