Question

Hello could u please help with this question??

A function is shown in the table.
x
g(x)
−2 2
−1 0
0 2
1 8
Which of the following is a true statement for this function? The function is decreasing from x = 0 to x = 1. The function is decreasing from x = −1 to x = 0. The function is increasing from x = 0 to x = 1. The function is increasing from x = −2 to x = −1.

Answer 1

The correct answer is c

Answer 2

*when looking at the intervals, order matters*

So these are the points of g(x):
(-2, 2)
(-1, 0)
(0, 2)
(1, 8)

And these are the answer choices:
a.) The function is decreasing from x = 0 to x = 1.
b.) The function is decreasing from x = −1 to x = 0.
c.) The function is increasing from x = 0 to x = 1.
d.) The function is increasing from x = −2 to x = −1.

Let's take a look at the first answer choice. It says that from x = 0 to x = 1, the y is decreasing. Well, when x = 0, y = 2 (from the point) and when x = 1, y = 8. So a.) is in fact wrong. The function is increasing from x = 0 to x = 1, not decreasing.

Let's look at the second choice. It says that the function is decreasing from x = 0 to x = -1. Let' look at the two points when x = -1 and x = 0.
(-1, 0)
(0, 2)
Well, starting from x = -1, the y is 0. And from 0, the y is 2. So the function is actually increasing at that interval. The second choice is incorrect.

And the third choice: from x = 0 to x = 1, the function is increasing. Look at the points.
(0, 2)
(1, 8)
The y starts at 2 then goes to 8. So the function is indeed increasing.

The third choice is correct! ^-^

(always double check all answers but I'll tell you right now the fourth one is incorrect)