Question

Exploration Graph $y=x^3$. Then on the same screen graph $y={(x-1)}^3+2$. Could you have predicted the result?

Short answer

The graph of the two functions on the same screen is

Yes, we could have predicted the graph of$y={(x-1)}^3+2$from the graph of$y=x^3$.

Step-by-step solution

Step 1. Given information

The graph of the functions $y=x^3$and $y={(x-1)}^3+2$on the same coordinate plane is drawn as

Step 2. Prediction

Both the graphs have the same shape, so yes we could have predicted the result.

As $1$is subtracted from the argument $x$and $2$is added to the output of the function $y=x^3$to get the function $y={(x-1)}^3+2$.

So the graph of $y={(x-1)}^3+2$is the graph of $y=x^3$shifted horizontally right by one unit and shifted vertically up by two units.