Question

Is it linear non linear a function or not a function:


1 x = 1 y

2 x = 8 y

3 x = 27 y

4 x = 64 y

5 x = 125 y

6 x = 216 y

7 x = ?

Answer 1

To determine whether the relationship \(x\) and \(y\) represent a function, and if it is linear or nonlinear, we will look for a consistent pattern.

The given ordered pairs appear to be:

1. \(x = 1, y = 1\) (which can be seen as \(1^3\))
2. \(x = 8, y = 2\) (which can be seen as \(2^3\))
3. \(x = 27, y = 3\) (which can be seen as \(3^3\))
4. \(x = 64, y = 4\) (which can be seen as \(4^3\))
5. \(x = 125, y = 5\) (which can be seen as \(5^3\))
6. \(x = 216, y = 6\) (which can be seen as \(6^3\))

From this pattern, we can see that \(y = \sqrt[3]{x}\), which is a specific function relating \(x\) and \(y\).

Now for \(x = 7\):
- To find \(y\), we can see that if \(y\) follows the pattern shown, then:
\[
y = \sqrt[3]{7}
\]

Thus, for each \(x\), each \(y\) corresponds to a unique \(y\), confirming that this is indeed a function.

### Function Analysis:
- **Is it a function?** Yes.
- **Is it linear?** No, because it is not of the form \(y = mx + b\). Instead, it's a cube root function.

### Conclusion:
The relationship described by your pairs is a function, and it is a nonlinear function (specifically a root function).