AP Calc BC Vocab Review

limit

a y-value which a function approaches as x approaches some value

function value

the y-value or output of the function

continuity

where the function’s y-value matches the limit; when the left limit is equal to the right limit

discontinuities

where the limit does not exist in the function; consists of holes, vertical asymptotes, and jumps

removable discontinuities

the type of discontinuity where the function has a limit, such as holes in the graph

nonremovable discontinuities

when the limit of the function does not exist; such as jumps, vertical asymptotes, or oscillations

Greatest Integer Function

where f(x) = [x] = the greatest integer less than or equal to x

Intermediate Value Theorem

if f(x) is continuous on interval [a, b] and k is any y-value between f(a) and f(b), then there is at least one x-value c between a and b such that f( c ) = k

horizontal shift

the graphing adjustment that occurs from y = f(x ± c)

vertical shift

the graphing adjustment that occurs from y = f(x) ± d

reflection across the y-axis

the graphing adjustment that occurs from y = f(-x)

reflection across the x-axis

the graphing adjustment that occurs from y = -f(x)

vertical stretch

the graphing adjustment that occurs from y = a * f(x); where a is positive and greater than 1

vertical squeeze

the graphing adjustment that occurs from y = a * f(x); where a is positive and less than 1

horizontal squeeze

the graphing adjustment that occurs from y = f(b * x); where b is positive and greater than 1

horizontal stretch

the graphing adjustment that occurs from y = f(b * x); where b is positive and less than 1

reflection of all points below the x-axis to above

the graphing adjustment that occurs from y = | f(x) |

eliminate all points on the left of the y-axis and reflect the right to the left

the graphing adjustment that occurs from y = f( | x | )

even

the label given to vertical asymptotes / holes / x-intercepts if the sign does not change across the asymptote / hole / x-intercept and determined by the group power

odd

the label given to vertical asymptotes / holes / x-intercepts if the sign changes across the asymptote / hole / x-intercept and determined by the group power

infinite limits

the name given to limits that do not exist at a vertical asymptote

limits at infinity

the name given to limits that approach a number along a horizontal asymptote

horizontal asymptote

the feature of a graph found using end behavior or comparing the highest degree term of the numerator to the highest degree term of the denominator

vertical asymptote

the feature of a graph found by identifying the denominator restrictions left over after reducing

hole

the feature of a graph found by identifying the denominator restrictions that cancel out

average rate of change

the slope between two points on a graph

squeeze theorem

derivative

the slope of a tangent line at a given x-value

limit definition of the derivative

alternate form of the limit definition of the derivative

equation of a Tangent line

nondifferentiability

when a derivative does not exist; places where there is a hole, a jump, a vertical asymptote, a sharp turn, or a vertical tangent

velocity function

derivative of a position function or integral of an acceleration function

acceleration function

derivative of a velocity function

position function

integral of a velocity function

displacement

the net change in position (final position - original position)

total distance

the total change in position by the object in a time interval (takes into account of all direction changes by finding the zeros of the velocity function and plugging in the zeros and endpoints into the position function)

speed

the absolute value of velocity

average velocity

displacement / elapsed time

average speed

total distance / elapsed time