Question

The table below gives approximate values for three functions, f, g, and h. One is exponential, one is trigonometric, and one is a power function. Determine which is which and find possible formulas for each.

$x$ | $-2$ | $-1$ | 0 | 1 | 2 |
---|---|---|---|---|---|

$f(x)$ | 4 | 2 | 4 | 6 | 4 |

$g(x)$ | $20.0$ | $2.5$ | $0.0$ | $-2.5$ | $-20.0$ |

$h(x)$ | $1.33$ | $0.67$ | $0.33$ | $0.17$ | $0.08$ |

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 9### First,

the values of $h(x)$, as x gets larger, seem to approach 0.

This indicates a possible exponential function with a base smaller than 1,

$h(x)=a\cdot b^{x}$

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