Question

Which table shows a function that is decreasing over the interval (−2, 0)?

Image for option 1

Image for option 2

Image for option 3

Answer 1

Answer: Table 3 shows that f(x) decreases in the interval (-2,0)

Explanation:

Decreasing function: A decreasing function is a function that decreases continuously for a given interval of values

If we see the interval (-2.0) in the first image

the value of f(x) decreases from 0 to -5 and then increases to 0

So it is not decreasing continuously over the interval

For the second image in the interval (-2,0) the value of f(x) increases from -15 to -5 but decreases to -20

So it is also not decreasing continuously for the given interval

For the third image

At x=-2, f(x)= 0

At x=-1, f(x)= -10

At x=0, f(x)=-24

Here the value of f(x) is continuously decreasing over the interval (-2,0)

Hence table 3 shows that the function is decreasing continuously over (-2,0)

Answer 2

Answer : Image 3

Which table shows a function that is decreasing over the interval (−2, 0)?

We look at the interval -2 to 0 on x

In option 1 table , f(x) is 0 then -5 and then becomes 0

It means -2 to -1 , f(x) decreases but from -1 to 0 y values increases

In option 2 table , f(x) is increasing from -15 to -5

In option 3 table, f(x) values goes on decreasing over the interval -2 to 0

So , option 3 table shows a function that is decreasing over the interval (−2, 0)