Question

The set of ordered pairs represents a

Answer 1

Answer:

The rule that represents the function is $y=x^2+1$ therefore the function is $f(x)=x^2+1$

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 $y=x^2+1$ 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

$f(2)=2^2+1=5$

$f(3)=3^2+1=10$

Therefore, the rule is correct, and the function is

$f(x)=x^2+1$