Question

Open the graphing tool again. Move the sliders for the functions y = (x − k)3 and y = x3 + k to any location you choose. Will these two graphs ever coincide? Why or why not?

Answer
The graphs meet only when k = 0. The horizontal and vertical translations position the graph in unique locations that will never otherwise be the same graph.

Answer 1

k=0

Explanation:

Answer 2

They will never coincide look at the attachment for the graph.

Explanation:

We have been given two equations:

`y=(x-3)^3`

And
`y=x^3+k`

Look at the attachment for the graph of the equation.

The given two equation will never coincide because their graph shows parallel lines.

And parallel lines never intersects.