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)
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