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# Module 23

### Exponential Functions

Question | Answer |
---|---|

To solve equations, what formula is used? | b^x=b^y |

To make this formula possible, the base "b" must be... | Positive, so b^x IS a real number for all real numbers x. |

Functions of the form are... | f(x)=b^x, where b>0. |

If b>0, b is NOT 1, and x is a real number, f(x)=b^x is called.. | Exponential Function |

When graphing... | Find and plot a few ordered pair solutions. Set up a table of values for each two functions. Then, connect a smooth curve. |

One-to-one function y-intercept (0,1) no x-intercept | f(x)=b^x, for b>1 |

domain: (-infinity,infinity) range: (0,infinity) | f(x)=b^x, for 0<b<1 |

The uniqueness of b^x can be used when: b>0 and b DOES NOT = 1, then... | b^x=b^y IS equivalent to x=y. |

When solving, each side of the equation must have.. | the same base, b^x=b^y |

We have equal exponents when the bases are the same and non-negative, this is called... | Uniqueness of b^x |

An example of the uniqueness of b^x is: 2^x=16, thus we would change 16 to 2^4 so x would equal... | x=4 |

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hannah96lee