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| | |1.1 & 1.2 Analyzing the Properties of Relations and Functions |off |

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| |Domain and Range |Graph each function using a graphing calculator. Analyze the graph to determine whether each function is | |

| | |even, odd or neither. | |

| |Write each set of numbers using interval notation | | |

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| |Sage and Scribe | | |

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| | | |Odd or |

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| |Odd or Even Functions |Write the domain and range of each graph |Domain |

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| |Graphs of functions can have y-axis or origin symmetry. Functions with these types of symmetry |a. |Range |

| |have special names. | | |

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| |Type of Function | | |

| |Algebraic Test | | |

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| |Functions that are symmetric with respect to the y-axis are called even functions. | | |

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| |For every x in the domain of f, f(-x)=f(x) | | |

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| |Functions that are symmetric with respect to the origin are called odd functions. | | |

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| |For every x in the domain of f, f(-x)=-f(x) | | |

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| |Is it a Function? |Use the graph of each equation to test for symmetry with respect to the y-axis and the origin. Support | |

| | |the answer numerically. Then confirm algebraically. | |

| |A function f from set A to set B is a relation that assigns to each element x in set A exactly one| | |

| |element y in set B |a. | |

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| |Vertical Line Test: a set of points in the coordinate plane is the graph of a function if each | | |

| |possible vertical line intersects the graph in at most one point. | | |

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| |Function Symmetry |Determine whether each relation represents y as a function of x. | |

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| |Graphs of relations can have two different types of symmetry. Graphs with line symmetry can be | | |

| |folded along a line so that the two halves match exactly. Graphs that have point symmetry can be |a. [pic] | |

| |rotated [pic]with respect to a point and appear unchanged. The two most common types of symmetry | | |

| |are shown below. | | |

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| |Graphically | | |

| |Graphically | | |

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| |The graph of a relation is symmetric with respect to the y-axis if and only if for every point (x,| | |

| |y) on the graph, the point (-x, y) is also on the graph. | | |

| |The graph of a relation is symmetric with respect to the origin if and only if for every point (x,| | |

| |y) on the graph, the point (-x, y) is also on the graph. |c. [pic] | |

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| |Model | | |

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| |Algebraically | | |

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| |Replacing the x value with a –x produces an equivalent equation. | | |

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| |Replacing the x value with a –x value AND the y value with a –y value produces an equivalent | | |

| |equation. | | |

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| |X & Y-intercepts |The x-intercepts of a function are also called the zeros of a function. The solutions of the | |

| | |corresponding equation are called the roots of the equation. To find the zeros of a function, set the | |

| |A point where a graph intersects the x or y axis is can an intercept. A y-intercept occurs where |functions equal to 0 and solve for the independent variable. | |

| |x=0. The graph of a function may only have one y-intercept. | | |

| | |Use the graph of each function to approximate its zero(s). Then find its zero(s) algebraically. | |

| |Use the graph of each function to approximate its y-intercept. Then find the intercept | | |

| |algebraically. |a. | |

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