Question

Graphs of functions on the interval [−4, 4] are depicted below. For each function, find:

1) The domain

2) Zeros of a function (the values of x where the function is zero)

3) Intervals where the function is positive and intervals where it is negative

Answer 1

Domain : [-4,4} or
`-4\leq x\leq 4`

Zeros of the function: (-2, 0, 2)

Intervals when function is positive: (0,2)

Intervals where function is negative: (-4,0), (2,4)

Explanation:

Domain can be defined as the input of all possible values of x in the given interval. We can se from the graph that minimum value of x is -4 while maximum value of x is 4. So

`-4\leq x\leq 4`

The value of function becomes 0 at three places, when x becomes -2,0 or 2

We can see that the function is negative throughout the interval (-4,0), then it become positive from (0,2), then it becomes negative again from (2,4)