Calculus Prerequisite vocabulary (Ch 1)
1.
2.
3.
4.
5.
Absolute Maximum – a point that represents the maximum value a function assumes over its
domain.
Absolute Minimum – a point that represents the minimum value a function assumes over its
domain.
Absolute Value Function - the function f(x) = |x| defined as a piecewise function
𝑥, 𝑥 < 0
𝑓(𝑥) = {
−𝑥,
𝑥≥0
Antilogarithm – x represents this, if log x=a, then x = antilog a
antiln x- the antilogarithm of a natural logarithm
6.
7.
Asymptotes – a line that a graph approaches but never intersects
Base a Logarithmic Function 𝑦 = 𝑙𝑜𝑔𝑎 𝑥, – The inverse of the base a exponential function
y = ax, 𝑎 > 0, 𝑎 ≠ 1
8.
10.
Composition of functions – A function is performed and then a second function is performed on
the result of the first function.
Compounded continuously, y = P ∙ert , where P= the initial investment, r is the interest rate as a
decimal, and t is time in years.
Common Logarithm – logarithms that use ten as the base and written y = log x
11.
Change of Base Formula - 𝑙𝑜𝑔𝑎 𝑛 =
12.
13.
14.
Constant Function – a function of the form f(x) = b.
Constant of Variation – the constant k used with direct or inverse variation
Continuous – A function is said to be continuous at point ( x 1 , y 1 ) if it is defined at that point
and passes through that point without a break.
Continuously Compounded Interest –
𝐴 = 𝑃𝑒 𝑟𝑡 , P is the initial amount, A is the final amount,
r is the annual interest rate, and t is time in years
9.
15.
16.
17.
𝑙𝑜𝑔𝑏 𝑛
𝑙𝑜𝑔𝑏 𝑎
20.
21.
Critical Point - points at which the nature of a graph changes
Decreasing Function – A function f is decreasing on an interval I if and only if for every a and b
contained in I, f(a) > f(b) whenever a<b.
Direct Variation – y varies directly as x n if there is some nonzero constant k such that y=k x n ,
n>0, the variable k is called the constant of variation.
Discontinuous - A function is said to be discontinuous at point ( x 1 , y 1 ) if there is a break in the
graph of the function at that point.
Domain – The set of abscissas.
e - a special irrational number approximately = 2.718. the base of natural logarithms
22.
End Behavior – the behavior of f(x) as x becomes very large.
23.
24.
25.
26.
Even Function - a function whose graph is symmetric with respect to the y-axis.
Everywhere Discontinuous – A function that is impossible to graph in the real number system.
Extremum – a maximum or minimum value of a function .
Exponential function with base a – a function in the form 𝑦 = 𝑎 𝑥 , where a is a positive real
number.
18.
19.
1
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
Exponential decay, y = ak, 0<a<1 and k>0, occurs when a quantity decreases exponentially over
time.
Exponential growth , y = ak, a >1 and k>0, occurs when a quantity increases exponentially over
time.
Function – A relation in which each element of the domain is paired with exactly one element in
the range.
Function Notation – f(x)
General linear equation – Ax + By = C (A and B not both 0)
Half-life of a radioactive element- the time requird for half of the radioactive nuclei present in a
sample to decay.
Horizontal Asymptote – The line y=b is a horizontal asymptote for a function f(x) if f(x) →b as x→∞
or as x→-∞.
Horizontal Line Test - a test used to determine if the inverse of a relation is a function.
Increasing Function – for every a and b contained in an interval I, f(a) < f(b) whenever a<b.
Increment - If coordinates change from (x1, y1) to (x2, y2), the increments in the coordinates are
∆x=x2-x1 and ∆y=y2-y1
Identity function f(x) = x
Infinite Discontinuity – as the graph of f(x) approaches a given value of x, f ( x ) becomes
increasingly greater.
Inverse Function –[fοg](x)=[ gοf](x) for all values of x
Inverse of f = f -1
Inverse Process – To find the inverse of a function, use this process to solve for y after switching
variables.
Iterate- each output of an iterated function
Iteration – the composition of a function and itself.
Inverse Relations – One relation contains the element (b,a) whenever the other relation contains
the element (a,b).
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.
Know the Definitions for the six trig functions, their inverses, and the domain & range of each.
Know the unit circle and the special angle ratios for Sine Cosine and Tangent from 00 to 3600.
1
48.
49.
50.
51.
52.
53.
54.
𝑛
𝑚
𝑛
𝑛
Know all the laws of exponents: for example: 𝑏 𝑛 = √𝑏 and 𝑏 𝑛 = √𝑏 𝑚 = ( √𝑏 )𝑚
Line Symmetry – Two distinct points P and P′ are symmetric with respect to a line l if and only if l is
the perpendicular bisector of segment PP′. A point P is symmetric to itself with respect to line l if
and only if P is on l.
Linear Function – a function defined by f(x)=mx+b, where m and b are real numbers.
Linear Inequality – a relation whose boundary is a straight line
Logarithm – y is called this in the function 𝑥 = 𝑎 𝑦
If 𝑙𝑜𝑔𝑎 𝑏 = 𝑐 𝑡ℎ𝑒𝑛 𝑎𝑐 = 𝑏
Maximum – a critical point of a graph where the curve changes from a increasing curve to a
decreasing curve.
2
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
Minimum – a critical point of a graph where the curve changes from an decreasing curve to a
increasing curve.
Monotonicity – A function is said to be monotonic on an interval I if and only if the function is
increasing on I or decreasing on I.
Natural logarithms – logarithms that use e as the base, written ln x
Odd Function - a function whose graph is symmetric with respect to the origin.
One to one function- Both the f(x) and f-1(x) it’s inverse pass the vertical and horizontal line test.
Parent Graph – an anchor graph from which other graphs in the family are derived.
Periodic function is a function where there exists a positive # p such that f(x + p) = f(x). the
smallest such value of p is the period of f.
Piecewise Function – a function in which different equations are used for different intervals of the
domain.
Point Discontinuity – When there is a value in the domain for which f(x) is undefined, but the
pieces of the graph match up.
Point of Inflection – a critical point of a graph where the graph changes its curvature from concave
down to concave up or vise versa.
Point Symmetry - Two distinct points P and P’ are symmetric with respect to a point M if and only
if M is the midpoint of segment PP’. Point M is symmetric with respect to itself.
Point-slope form – the equation of the line that contains the point with coordinates ( x 1 , y 1 ) and
having slope m written in the form y  y 1 = m ( x  x 1 )
67.
68.
Power function – a function in the form 𝑦 = 𝑥 𝑏 , 𝑤ℎ𝑒𝑟𝑒 𝑏 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟
Radian Measure of a central angle in a unit circle is the length of the arc it cuts from the circle
69.
70.
71.
72.
73.
74.
75.
76.
Range – The set of ordinates.
Relation – A pairing of elements of one set with elements of a second set.
Regression analysis – the process of finding a regression curve to fit thedata
Relative Extremum – a point that represents the maximum or minimum for a certain interval.
Relative Maximum - a point that represents the maximum for a certain interval.
Relative Minimum - a point that represents the minimum for a certain interval.
Scatter Plot – the plotting of paired numbers on a Cartesian coordinate system.
2𝜋
Sinusoid function can be written in the form 𝑓(𝑥) = 𝐴 sin ⟦ 𝐵 (𝑥 − 𝑐)⟧ + 𝐷, where |A| is the
amplitude, |B| is the period, C is the horizontal shift, and D is the vertical shift.
Slope – the ratio of the change of the ordinates of the points to the corresponding change in the
77.
abscissas.
78.
79.
80.
81.
82.
83.
m=
y2  y1
x2  x1
Slope-intercept form - The equation of a line with slope, m, and y-intercept, b, written in the
form y=mx+b.
Standard form – A linear equation written in the form Ax + By + C = 0, where A, B, and C are real
numbers and A and B are not both zero.
Vertical Line Test – If every vertical line drawn on the graph of a relation passes through no more
than one point of the graph, then the relation is a function.
x-intercept - The point where the line crosses the x axis; the zero of a function, the solution
y-intercept
- The point where the line crosses the y axis.
Zeros of the function f –
values of x for which f(x) = 0
3