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AP Calc Preparation
flashcards for going in AP Calculus AB
76
Mathematics
12th Grade
08/10/2016
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Term
Domain:
 Definition
x, input values, the independent variable, time
Term
Range:
 Definition
y, output values, dependent variable
Term
Evaluate:
 Definition
you are given x, use the function to determine the y values
Term
Derivative:
 Definition
the slope of a tangent line
Term
Difference quotient:
 Definition
an input value function that includes both x and Δx that when simplified, all terms which do not have a Δx cancel out
Term
Vertical line slope:
 Definition
a vertical line has no slope
Term
Horizontal line slope:
 Definition
a horizontal line has zero slope
Term
Slope:
 Definition
a rate of change
Term
Average rate of change:
 Definition
slope between two points
Term
Slope intercept form:
 Definition
y = mx + b
Term
Point slope form:
 Definition
y - y₁ = m(x - x₁)
Term
Standard (general) form:
 Definition
Ax + By = C
Term
3 domain restrictions:
 Definition
a) denominator ≠ 0, b) radicand ≥ 0, c) for a natural log of x, x ＞ 0
Term
Including these points -3,2:
 Definition
[-3,2]
Term
Not including these points -3,2:
 Definition
(-3,2)
Term
Union:
 Definition
written as “U” joins two sets of coordinates
Term
Even function:
 Definition
has the property that f(-x) = f(x)
Term
Odd function:
 Definition
has the property that f(-x) = -f(x)
Term
Piecewise function:
 Definition
also called a step function, it is broken into different segments based on domain restrictions, a function made up of multiple other functions
Term
Composite functions:
 Definition
when the range of one function is used as the domain of a second function, written as f(g(x)) or (f ⚬ g)(x)
Term
Exponential model equation:
 Definition
y = abˣ
Term
Rate of growth:
 Definition
when b>1
Term
Rate of decay:
 Definition
when 0<b<1
Term
Exponential model initial value:
 Definition
abbreviated “a” in the Exponential model
Term
General form of a conic section:
 Definition
Ax² + By² + Cx + Dy +Exy + F = 0
Term
Equation of a conic circle:
 Definition
(x² / r²) + (y² / r²) = 1
Term
Equation of a conic ellipse:
 Definition
(x² / a²) + (y² / b²) = 1
Term
Equation of a conic horizontal hyperbola:
 Definition
(x² / a²) + (y² / b²) = 1
Term
Equation of a conic vertical hyperbola:
 Definition
(y² / a²) + (x² / b²) = 1
Term
Vertical line test:
 Definition
if a graph of a function, f(x), passes the test, it is a function, as it has only one output (y value) for every input (x value)
Term
Horizontal line test:
 Definition
If a function has an inverse, it will also pass the horizontal line test, meaning for every x value, it only has one y value
Term
Notion for a function’s inverse:
 Definition
f⁻¹ (x)
Term
Rule for having an inverse:
 Definition
if you plug a into f(x), and get out b, you then plug b into  f⁻¹ (x) and get out a, the two functions are inverses
Term
Definition of a logarithm:
 Definition
logₐx = y, aʸ = x
Term
Inverse property of a logarithm:
 Definition
a^(logᵤx) = x, logᵤaˣ = x
Term
Logarithm of a power:
 Definition
logᵤ(xʸ) = ylogᵤx
Term
Change of base formula:
 Definition
logᵤx = (lnx)/(lnu)
Term
Logarithm of a product:
 Definition
logᵤ(xy) = logᵤx + logᵤy
Term
Logarithm of a quotient:
 Definition
logᵤ(x/y) = logᵤx - logᵤy
Term
Logarithm equal to one:
 Definition
Logᵤx = 1, logₓ1 = 0
Term
Determinate form:
 Definition
you can substitute a value for x and get out a value for y
Term
Indeterminate form 0/0:
 Definition
you will get out 0/0 when you plug in a value for x, you can factor the equation to get a function in determinate form
Term
Indeterminate form #/0:
 Definition
you will get out #/0, meaning the function is not defined at the inputted value, you will have a vertical asymptote
Term
A in the equation f(x) = Asin(Bx - C) + D:
 Definition
vertical scaling, stretches or squeezes the graph up or down, multiply every y value by a, flip if a is negative and multiply by the value of a
Term
B in the equation f(x) = Asin(Bx - C) + D:
 Definition
horizontal scaling, squeezes or stretches right/left, multiply every x value by its inverse (1/b), flips is b is negative
Term
C in the equation f(x) = Asin(Bx - C) + D:
 Definition
horizontal translation, move the graph left or right, right if the sign in the equation is negative, left if the sign in the equation is positive
Term
D in the equation f(x) = Asin(Bx - C) + D:
 Definition
vertical translation: moves the graph up or down, up if the sign in the equation is positive, down if the sign in the equation is negative
Term
A in the equation af(b(x+c)) + d:
 Definition
vertical scaling, multiply every y value by a
Term
B in the equation af(b(x+c)) + d:
 Definition
horizontal scaling: multiply every y value by 1/b (the inverse of b), flips over the y axis if b is negative
Term
C in the equation af(b(x+c)) + d:
 Definition
horizontal translation: move each x value to the right if the sign in the equation is negative, move each x to the left of the sign in the equation is positive
Term
D in the equation af(b(x+c)) + d:
 Definition
vertical translation: move each y value up if positive, or each y value down if negative
Term
 Definition
y = x
Term
[image]
 Definition
y = x², graph
Term
Y = x²
 Definition
parabola
Term
y = x
 Definition
linear
Term
[image]
 Definition
Y = ⎡x, graph
Term
Y = ⎡x
 Definition
linear
Term
[image]
 Definition
Y = 1/x, graph
Term
[image]
 Definition
Y = 1/x², graph
Term
Y = 1/x
 Definition
reciprocal graph
Term
[image]
 Definition
Y = |x|, graph
Term
Y = |x|
 Definition
absolute value
Term
[image]
 Definition
Y = [x], graph
Term
Y = [x]
 Definition
step function, piecewise graph
Term
[image]
 Definition
y = sinx
Term
[image]
 Definition
y = cosx
Term
[image]
 Definition
y = tanx
Term
[image]
 Definition
y = cotx
Term
[image]
 Definition
y = secx
Term
[image]
 Definition
y = cscx
Term
Y = x²
 Definition
parabola
Term
y = x
 Definition
linear
Term
Y = ⎡x
 Definition
linear
Term
Y = 1/x
 Definition
reciprocal graph
Term
Y = |x|
 Definition
absolute value
Term
Y = [x]
 Definition
step function, piecewise graph
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