Chapter 2: Q. 65 (page 103)

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

Short Answer

Expert verified

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.

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Prediction

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Exploration Graph y=x3. Then on the same screen graph y=(x-1)3+2. Could you have predicted the result?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Prediction

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

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