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# Chapt 3

Term | Definition |
---|---|

Point symmetry | A figure that has this symmetry can be rotated 180 degrees about the point and appears unchanged. |

Symmetry with respect to the origin | F(-x) =- f(x) |

Symmetry with respect to the x-axis | Tested by substituting (a,b) and (a, -b) into the equation produces equivalent equations. |

Symmetry with respect to the y- axis | Tested by substituting (a,b) and ( -a,b) into the equation produces equivalent equations |

Symmetry with respect to the y=x line | Tested by substituting (a,b) and (b,a) into the equation produces equivalent equations |

Symmetry with respect to the Y =-x | Tested by substituting (a,b) and (-b,-a) into the equation produces equivalent equations |

Even function | Functions whose graphs are symmetric with the y-axis. Tested substituting ( -a,b) |

Odd function | Functions whose graphs are symmetric with respect to the origin. F(-x) = f( -x). Can rotate the graph of the function by 180 degrees and it appears unchanged. |

Parent graph | The basic graph that is transformed to create other members in a family of graphs |

Reflection of y = -f(x) | Reflected over the x-axis |

Reflection of y = f(-x) | Reflected over the y- axis |

Translation of y = f(x) + c | Translates the graph up c units |

Translation of y = f(x) - c | Translates the graph down c units |

Translation of y = f( x + c) | Translates the graph c units left |

Translation of y = f(x - c) | Translates the graph c units right |

Change to the parent graph y=f(x), c >0 Y = c f(x), c >1 | Expands the graph vertically resulting in a more narrow graph |

Change to the parent graph. y = f(x), c > 0 Y = c f(x), 0<c<1 | Compresses the graph vertically resulting in a wider graph |

Change to the parent graph y=f(x), c>0 Y = f( cx), c>1 | Compresses the graph horizontally resulting in a more narrow graph |

Change to the parent graph y = f(cx), 0<c<1 | Expands the graph horizontally resulting in a wider graph |

Inverse relations | Only if one relation contains the elements (a,b) and the other relation contains the elements (b,a) |

Horizontal line test | A test used to determine if the inverse of a relation is a function. If every horizontal line intersects the graph in at most one point, then the inverse is a function. |

Asymptote | It is a line the function approaches, but never crosses. |

End Behavior | The behavior of a function as x goes to positive infinite and as x goes to negative infinite. Written like x-> + infinite, y-> x-> - infinite, y-> |

Maximum | This is a critical point where the curve changes from an increasing curve to a decreasing curve. |

Minimum | This is a critical point where the curve changes from a decreasing curve to an increasing curve. |

Inverse | It is shown when a function is rotated about the line y = x. the equation can be found by switching the x's and y'x and solving for y. |

Critical point | It is the part of the graph where the nature of the graph changes; this includes minimums, maximums, and points of inflection. |

Absolute minimum | Is a minimum that is the smallest y-value of the entire function. |

Absolute maximum | Is the maximum that has the largest y-value of the entire function. |

Discontinuous | When a function has a break, hole, or is undefined at any point. |

Point of Inflection | When a function has a critical point where the graph changes its curvature form concave down to concave up or vice versa. |

Continuous | A function is said to be this at point(x1,y1) if it id defined at that point and passes through the point without a break. |

Monotonicity | A function is this on an interval I if and only the function is increasing on I or decreasing on I. |

Relative maximum or minimum | A point that represents the maximum or minimum for a certain interval. |

Jump discontinuity | The graph of f(x) stops and then begins again with an open circle at a different range value for a given value of the domain. |

Infinite Discontinuity | As the graph of f(x) approaches a given value of x, f(x) becomes increasingly large without bound. |