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Chapt 3

TermDefinition
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.
Created by: Ohs-Kays