Question

Function k is a continuous quadratic function that includes the ordered pairs shown in the table .

Answer 1

Complete question is;

Function k is a continuous quadratic function that includes the ordered pairs shown in the table. (-1,5), (0,8); (1,9), (2,8); (3,5) (4,0) Over which interval of the domain is the function Increasing?

A (1, ∞)

B. (-∞,1)

C (-∞, ∞)

D. (-∞,9)​

Answer:

Option B - (-∞ , 1)

Step-by-step explanation:

From the ordered pairs given, we observe the following:

From (-1, 5) to (0, 8);

In this, 8 is more than 5, thus there is an increase.

From (0, 8) to (1, 9);

In this, 9 is more than 8, thus there is an increase.

From (1,9) to (2, 8);

In this, 8 is less than 9, thus there is a decrease.

Looking at all the ordered pairs, we can see that f(0) = 8 and f(2) = 8.

Thus, we can say that; f(0) = f(2)

This means that our maximum value is likely in the middle of 0 and 2.

Now, from all the ordered pairs, f(1) = 9 is the maximum value of the function.

It now means that when x = 1, the direction of the function changes.

We have seen that at points before x = 1 the function was increasing but after that point the function will begin decrease.

Thus, we can conclude that in all the values that fall in the range of x < 1, the quadratic function will be increasing.

So, the correct answer among the given options is: (-∞ , 1)