Question

1. Graph the equation y=-2x - 3| + 1. State the domain and range as well as the intervals over which the function is increasing and decreasing. y $ Domain: 12 구 Range: 5 4 3 12 군 Increasing interval: -9 - - -5 -4 -3 -2 -1 5 8 7 8 gx 2 2 Decreasing interval: chen -Z -9 M U:

Answer 1

since the function has an absolute value means that we have to graph the positive and negative form, also that it has to be moves 3 units to the right, 1 unit up and has a scale factor of -2.

final function should look like this

The domain of the function is all. values in x that the function can take place in, in this case it means that the domain will be:

`(-\infty,\infty)`

the range is all values of the images in x, in this case there is a maximun value which is 1, meaning that the range will be

`(-\infty,1\rbrack`

the increasing interval will be when the values tend to get higher values on the y axis, and the decreasing interval will be the contrary, according to this:

`\begin{gathered} (-\infty,3\rbrack\text{ increasing interval} \\ \lbrack3,\infty)\text{ decreasing interval} \end{gathered}`