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Chapt 3

Quiz yourself by thinking what should be in each of the black spaces below before clicking on it to display the answer.
        Help!  

Term
Definition
Point symmetry   A figure that has this symmetry can be rotated 180 degrees about the point and appears unchanged.  
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Symmetry with respect to the origin   F(-x) =- f(x)  
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Symmetry with respect to the x-axis   Tested by substituting (a,b) and (a, -b) into the equation produces equivalent equations.  
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Symmetry with respect to the y- axis   Tested by substituting (a,b) and ( -a,b) into the equation produces equivalent equations  
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Symmetry with respect to the y=x line   Tested by substituting (a,b) and (b,a) into the equation produces equivalent equations  
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Symmetry with respect to the Y =-x   Tested by substituting (a,b) and (-b,-a) into the equation produces equivalent equations  
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Even function   Functions whose graphs are symmetric with the y-axis. Tested substituting ( -a,b)  
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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.  
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Parent graph   The basic graph that is transformed to create other members in a family of graphs  
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Reflection of y = -f(x)   Reflected over the x-axis  
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Reflection of y = f(-x)   Reflected over the y- axis  
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Translation of y = f(x) + c   Translates the graph up c units  
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Translation of y = f(x) - c   Translates the graph down c units  
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Translation of y = f( x + c)   Translates the graph c units left  
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Translation of y = f(x - c)   Translates the graph c units right  
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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  
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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  
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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  
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Change to the parent graph y = f(cx), 0<c<1   Expands the graph horizontally resulting in a wider graph  
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Inverse relations   Only if one relation contains the elements (a,b) and the other relation contains the elements (b,a)  
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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.  
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Asymptote   It is a line the function approaches, but never crosses.  
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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->  
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Maximum   This is a critical point where the curve changes from an increasing curve to a decreasing curve.  
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Minimum   This is a critical point where the curve changes from a decreasing curve to an increasing curve.  
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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.  
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Critical point   It is the part of the graph where the nature of the graph changes; this includes minimums, maximums, and points of inflection.  
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Absolute minimum   Is a minimum that is the smallest y-value of the entire function.  
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Absolute maximum   Is the maximum that has the largest y-value of the entire function.  
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Discontinuous   When a function has a break, hole, or is undefined at any point.  
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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.  
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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.  
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Monotonicity   A function is this on an interval I if and only the function is increasing on I or decreasing on I.  
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Relative maximum or minimum   A point that represents the maximum or minimum for a certain interval.  
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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.  
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Infinite Discontinuity   As the graph of f(x) approaches a given value of x, f(x) becomes increasingly large without bound.  
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