Question

#15If you do not know college algebra, please say so and let me move on.

Answer 1

In order to graph the functiom we need to identify the parent function and the vertical and horizontal shifts that might be done to the function.

In this case we see that the parent function is a cubic function since the greater degree is 3

`g(x)=x^3`

this means that f(x) is a transformation of g(x)

then

the horizontal shifts since there is sum inside the parentheses the shift will be 1 unit to the left.

the vertical shift will be 1 unit up since there is a sum outside the parentheses.

and finally since there is a - it means that the function is reflected over the x-axis

the parent function will be the red line and the function #15 is the blue line.

In order to find points we can tabulate the values for given xs' and construct the graph.

Start by making a table like this:

now since the function is given we can replace x with the values and find y

`\begin{gathered} y=-(x+1)^3+1 \\ y=-(-6+1)^3+1 \\ y=-(-5)^3+1 \\ y=-(-125)+1 \\ y=125+1 \\ y=126 \end{gathered}`

then after tabulating values should look like this

Now looking at the graph on the blue function we can see that the function is decreasing until reaching x=-1, however after that the function will continue to decrease but at a different rate, which means that over the interval

`(-\infty,\infty)`

the function will be decreasing