Answer
$(a)$ See the image below.
$(b)$ The function is not one-to-one
$(c)$
Minimum points:
$(-1.61,-27.18)$; $(1.43, -11.93)$
Maximum point:
$(0.18, -2.55)$
$(d)$ The range is $[-27.18, +\infty)$
$(e)$
Decreasing:
$(-\infty, -1.61)$
$(0.18, 1.43)$
Increasing:
$(-1.61, 0.18)$
$(1.43, +\infty)$
Work Step by Step
$(a)$ See the image above.
To draw the graph of the function, we can use graphing calculator. An appropriate viewing rectangle would be the view in which we will be able to see every main point of the function. The viewing rectangle of $[-3.5, 3.5]$ $[-30, 20]$, gives us the full picture we need.
$(b)$ Using the Horizontal Line Test we can see that the function is not one-to-one.
There is a horizontal line that crosses the graph of the function more than one time.
$(c)$ From the graph we can see the following points:
Minimum points:
$(-1.61,-27.18)$; $(1.43, -11.93)$
Maximum point:
$(0.18, -2.55)$
$(d)$ From the graph we see that the function has absolute minimum value at approximately $-27.18$ and then it goes upward to the infinity. So the range is $[-27.18, +\infty)$
$(e)$ From the graph we can see the following:
Decreasing:
$(-\infty, -1.61)$
$(0.18, 1.43)$
Increasing:
$(-1.61, 0.18)$
$(1.43, +\infty)$
