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# Calc 8/23

### Quiz Review

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

What is the DOMAIN of a function? | The set of all input values. The X values. |

What is the RANGE of a function? | The set of all output values. The Y values. |

How many values of X are there for each value of Y in a standard function? | THERE CAN BE ONLY ONE! |

How do you determine if a graph of data is a function? | If it passes the VERTICAL LINE TEST. |

How many values of Y are there for each value of X in an INVERSE function? | THERE CAN BE ONLY ONE! |

Define the characteristics of an increasing function. | As X increases, Y increases. "Slopes" are positive. |

Define the characteristics of a decreasing function. | As X increases, Y decreases. "Slopes" are negative. |

How many radians are in 180º? | There are pi radians in 180º. |

Define 1 radian. | 1 radian is the measurement of the angle, theta, in the sector of a circle when radius length is equal to arc length. |

What is the formula for arc length of a sector? | Arc length is equal to the radius times theta. L=rΘ |

List the 5 types of functions. | Trigonometric, exponential, logarithmic, polynomic, rational. |

List the six trigonometric functions and what their purpose is. | The trigonometric functions sin, cos, tan, cot, sec, and csc are used to measure angles and area. |

What is the format of an exponential function? | e^x or a^x |

What is the format of a logarithmic function? | logX in base a or lnX |

What is the format of each term in a polynomial? | aX^n Where a is any real number, X is a variable, and n is 0 or any positive integer. |

Define a rational function. | A ratio of two polynomials. Ex: (3x^3+2x^2+x)/(x^2+3x+9) |

Define a term. | A quantity that is added or subtracted. |

Define a factor. | A quantity that is multiplied or divided. |

Can you cancel terms with factors? | One does not simply cancel a term with a factor. |

What are the two methods to find the domain of a function? | Eliminate X values that create a 0 denominator. Eliminate sections of the real number spectrum which create a negative quantity under a radical with an even root. |

If a function is even, how is it symmetric? | With respect to the Y-axis. |

If a function is odd, how is it symmetric? | With respect to the origin. |

How do you tell if a function is even? | Negate X and simplify. You should get the original function. |

How do you tell if a function is odd? | Negate X and simplify. You should get the opposite of the original function. |

If f(X) is periodic, what happens when you add the period to X? | You get f(X). |

What should you exclude in the domain of a combined function? Ex: f+g(X) | X values of each individual function and additional X values in the combined form. |

What are the rules for the domain of a composite function? Ex: f(g(X)) | The domain of the composite must include the domain of its inner function. The domain of the composite can NEVER be greater than that of the inner function. |

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