Chapter 1.2, Problem 33E

Solution

To identify: graph the function and intervals on which the function is increasing,

decreasing, or constant.

The function is

Decreases: $(-\infty ,1]$

Increases: $[1,\infty )$ .

Given information: 

The function $g\left(x\right)=3-{\left(x-1\right)}^2$ .

Calculation:

Graph of

  $g\left(x\right)=3-{\left(x-1\right)}^2$

Let $y=g\left(x\right)$ .

Putting the value of $x=1$ then $y=3$ .

And $x=-1$ then $y=-1$

And $x=-2$ then $y=-6$

And $x=2$ then $y=2$

Plot the graph:

  

Therefore, the function increases in the interval $(-\infty ,1]$ and decreases in the interval $[1,\infty )$