Rewrite 27x−81−−−−−−−√3−5 to make it easy to graph using a translation. Describe the graph.

Answer 1

To make the equation easy to graph using a translation, we can rewrite it as:

27(x - 3)^(1/3) - 5

By subtracting 3 inside the cube root, we perform a translation of 3 units to the right.

The graph of this equation will be a shifted cube root function. The parent function of a cube root function is y = ∛x. By shifting the graph 3 units to the right, the graph will be moved to the right, and the point (3, 0) will be the new vertex.

Additionally, the graph will be vertically stretched or compressed depending on the coefficient before the cube root. In this case, the graph will be vertically stretched by a factor of 27. This means that the graph will become steeper.

Overall, the graph will be a vertical stretch of the cube root function y = ∛x, moved 3 units to the right, and vertically stretched by a factor of 27.