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The data in the table can be modeled using the function y = A tan(Bx).

Input | output | input | output |

-8 | - infinity | 1 | 1.8 |

-7 | -44.2 | 2 | 3.6 |

-6 | -21.2 | 3 | 5.9 |

-5 | -13.2 | 4 | 8.8 |

-4 | -8.8 | 5 | 13.2 |

-3 | -5.9 | 6 | 21.2 |

-2 | -3.6 | 7 | 44.2 |

-1 | -1.8 | 8 | infinity |

0 | 0 |

1. State the value of A.

a. 11.3

b. 7

c. 4.7

d. 3.1

2. State the location of asymptotes.

a. 16k, k € Z

b. 8 + 4k, k € Z

c. 8k, k € Z

d. 8 + 16k, k € Z

3. Use the model to evaluate the function at x = 10.

a. -6.6

b -15.9

c. -21.2

d. -9.9

Guest Sep 6, 2017

edited by
Guest
Sep 6, 2017

#2**+2 **

The data in the table can be modeled using the function y = A tan(Bx).

I am going to assume that this question is in degrees.

Two of the asymptotes lie at \(x=\pm \frac{90}{B}\)

The asymptotes here lie at x= 8 and x= -8

So

8=90/B

B=90/8 = 11.25

I think the first question actually meant for you to find B not A.

---------------------

Now one asymptote is at x=-8 then x=8 so the next one will be at x=8+16=24

So

the asymptotes occur at x=8+16K where k is an integer.

--------------------

3. Use the model to evaluate the function at x = 10.

f(10)=f(-6)=-21.2

--------------------

Here is the graph, maybe it will help you though it was not necessary for answering those questions.

Melody Sep 9, 2017