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# Final Exam Cards

### These will be supplimental for a final exam

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

What are Monomials? How do you solve them? | Monomials: Are algebraic expressions that have only 1 term. -Multiply Numerators, and simplify. -Multiply Denominators and simplify. -Divide the Coefficients. -Subtract like bases (From numerator and denominator) To simply and get final answer. |

What are Binomials? How do you solve them? | Binomials: Bi = 2. These will have two terms. - Simplify! -Find the multiples of both numbers. -Set one to Positive, and the other to negative. -2x-49 (x-7)(x+7) = The "Zeros" |

What are Trinomials? How do you solve them? | Trinomials: Expressions with three terms. - Look at the middle term. What TWO numbers will add to get that, and multiply to get the LAST term? -Simply figure this out, and you will get your zeros. |

Who is BeN? Why does he help in exponential equations? | Ben is Base - The base of the logarithm. Exponent - The small number above. Number - The Number or output. - This tells us how an exponential equation is composed. BASE,EXPONENT, then NUMBER. |

Who is BNE, or Bennie? How does it help with logarithmic equations? | BNE = Base Number Exponent -To convert an exponential equation into a logarithmic equation. -Replace BEN with BNE. |

What do you need to include when graphing polynomial finctions? | 1.) Zeros 2.) Test points 3.) The End behavior 4.) Graph (Of course.) |

How do you figure out the turning points of a polynomial? | The degree. (Highest exponent.) Minus 1 will determine this. |

What is a Turning point? | An X value where a local maximum or minimum occurs. |

How do you determine the End Behavior of a graph? | -POSITIVE and EVEN. Both points go up. -POSITIVE and ODD. Right arm goes up, left arm goes down -NEGATIVE and EVEN. Both points go down. -NEGATIVE and ODD. left arm goes down right arm up |

What is a Vertical Asymptotic? | VERTICAL lines that occur from the DENOMINATOR of a rational. |

How can you find ALL the zeros of a polynomial? | 1.)Synthetic Division 2.)Long Division 3.)Factoring 4.)Graphing. - If having trouble on one, go to another. |

What is a Function? | -Passes vertical line test -Has only ONE input. One unique X value. |

How do you know when there's a horizontal asymptote? | This will only happen when there is a VERTICAL shift. |

How do you solve a peace wise function? | These are like puzzles! -You must look if the greater than or less than has a line under it. -Line = Closed circle. No line = Open Circle. -solve the peace wise in the way the problem asks you to. x>0 means that it will be ALL of the values over 0. |

Quadratic formula. | x=-b±sqrt/b^2-4ac 2a REMEMBER -B- No bees! ±2 4 - AIR CONDITIONING 2a 2 on top and 2a on bottom! |

what is e? Where can You find it? | "Natural Base" 2nd key, then division key. e = Approximately 2.718 |

What is the vertex formula? | a(x-h)^2+k |

When should I use Synthetic Division, as opposed to Long Divison? | Synthetic division for smaller polynomials. 2x-4 is an example. Long division can do ALL other polynomials, but takes MUCH LONGER. |

What are One to One Functions? | Has EXACTLY 1 X value and 1 Y Value. -Passes Horizontal AND Vertical line test. |

What is a negative exponent? Why do we NOT want this? | A Negative exponent = the reciprocal of the number it's in front of. 1.) Simplify ALL Negative exponents to the reciprocal . 2.) Divide the fractions and simplify. 3.) Times ALL Denominators by each part. 4.) Simplify and solve. |