Question

Make a t-table for each function for the x-values 2 through 6. Which function grows the fastest?

a: y = x

B) y = x2

C) y = x3

D) y = 4x

Answer 1

To solve the problem, we need to create t-tables for each of the given functions for the x-values 2 through 6, and then compare the values of y to determine which function grows the fastest.

For function y = x:

| x | y |

|-------|-------|

| 2 | 2 |

| 3 | 3 |

| 4 | 4 |

| 5 | 5 |

| 6 | 6 |

For function y = x^2:

| x | y |

|-------|-------|

| 2 | 4 |

| 3 | 9 |

| 4 | 16 |

| 5 | 25 |

| 6 | 36 |

For function y = x^3:

| x | y |

|-------|-------|

| 2 | 8 |

| 3 | 27 |

| 4 | 64 |

| 5 | 125 |

| 6 | 216 |

For function y = 4x:

| x | y |

|-------|-------|

| 2 | 16 |

| 3 | 64 |

| 4 | 256 |

| 5 |1024 |

| 6 |4096 |

From the tables, we can see that the function y = 4x grows the fastest, as its values of y increase much more rapidly than the other functions as x increases. Therefore, the answer is D) y = 4x.

Explanation: