Question

Which of the following is the graph of y=-(x-2)^3-5

Answer 1

For this type of problem, go back to basic learning about shift to the right or left, up or down.
then check with desmos.com

Answer 2

We are given a function y=f(x) as:

`y=f(x)=-(x-2)^3-5`

Clearly the function f(x) is a cubic function.

This function could be formed by the transformation of the parent function:

`f(x)=x^3`

by firstly shifting it to the left by 2 units and then reflecting it across x-axis and then translating it 5 units down.

The graph of the function passes through the point:

(0,3) and (0.29,0).

Also the end behavior of the function is that it tends to infinity when x→ -∞ and y→ -∞ when x→ ∞.