Question

need help What are the intervals that it's increasing, decreasing, and constant?What is the range of the function?Is the function odd and even?

Answer 1

The domain of a function is the set of values of x for which the function is true.

To determine the domain of the function, you have to identify the values of x that correspond to the function.

The function starts at x= -3 and ends at x= 3, so the domain of the function is all values of x between -3 and 3.

Written using interval notation, the domain of the function is:

`{}[-3,3]`

This function can be divided into four parts.

The first part goes from x=-3 to x=-1, within this interval the function has a negative slope, which means that for the interval [-3,-1] the function decreases.

The second part of the function goes from x=-1 to x= 0, within this interval [-1,0] the function has a positive slope, which means that the function increases.

The third part of the function goes from x=0 to x=1, within this interval [0,1] the function has a negative slope, so the function decreases.

The fourth part of the function goes from x=1 to x=3, within this interval [1,3] the function has a positive slope, which means that the function increases.

Range

The range of the function is the set of values of y for which the function is true.

This function takes a value between y=0 and y=1, so the range of the function expressed in interval notation is:

`[0,1]`

A function is even when it is symmetrical with respect to the y-axis, and it can be considered to be odd when it is symmetrical about the x-axis.

If there is symmetry about the y-axis, then both parts of the function will look like a reflection.

In this case, the function is symmetrical about the y-axis, so you can conclude that this is an even function.