AP Calc Accumulative Flashcards
Describe the line and give the slope of:
y = 3?
Horizontal
Slope= 0
What is the point slope form of a linear equation?
y2 - y1 = m(x2 -x1)
Describe the line and give the slope of:
x = 4
Vertical Line
Undefined slope
What is the slope of any line that is perpendicular to the linear equation with slope m?
-1/m
(the inverse and opposite sign of the parent function)
What is the formula for finding the slope of a line?
m= Δy/Δx
or
m= (y2-y1)/(x2-x1)
Does the equation shown represent a function?
x2 + y2 = 4
No, this equation has term where “y” is raised to an even power. Thus, this equation is not a function, instead it is a circle.
If a function is odd the f(-x) =
-f(x)
If a function is even then f(-x) =
f(x)
What is the domain of f(x) = x / x2 - 1
x ≠ ± 1
The denominator of a rational function cannot equal zero.
What is the domain of f(x) = 3√x + 1
All real numbers or (-∞ , ∞ ) Any radical function that has an odd index number will have a domain of all real numbers.
Identify any horizontal and vertical asymptotes of f(x) = 3x + 1 / 2x2 - 2
y = 0
x = 1, -1
the exponent in the denominator is greater than the numerator thus the HA is y = 0
using 1 and -1 for x makes it so the denominator equals 0
Identify any horizontal and vertical asymptotes of f(x) = 3x2 + 1 / 4x2 - 16
y = ¾
x= 2, -2
¾ is the answer because they have the same exponents thus they are taking the fraction of coefficients for the HA
Identify any horizontal and vertical asymptotes of f(x) = x4 + 1 / x2 + 4
NONE
The exponent in the numerator is greater than the denominator, there is no HA
VA: can’t take the square root of a negative number
What is the domain of f(x) = x + 1 / x2 - 1
x ≠ ± 1
y = 3(2)x is exponential…
Growth
y = (¾)x is exponential…
Decay
y = 4(2)-x is exponential…
Decay
y = (½)-x is exponential…
Growth
Write 53 = 125 in Logarithmic form
Log5125 = 3
Write log168 = ¾ in exponential form
16¾ = 8
What is the domain of log(x - 4)?
x > 4
Cannot have a log(0) or a log(negative)
What is the Change of Base formula?
logbM = logaM / logaB
logb (MN)
= logbM + logbN
logb (M / N)
= logbM - logbN
logb (Mp)
= plogbM
Definition of
secθ =
cscθ =
cotθ =
secθ = hypotenuse/ adjacent = r/x = 1 / cosθ
cscθ = hypotenuse/ opposite = r/y = 1 / sinθ
cotθ = adjacent / opposite = x/y = 1 / tanθ
Fundamental identities: Reciprocal
secθ = 1/cosθ cosθ= 1/ secθ
cscθ = 1/ sinθ sinθ= 1/ cscθ
cotθ = 1/ tanθ tanθ= 1/ cotθ
Fundamental identities: Quotient
tanθ = sinθ / cosθ
cotθ = cosθ / sinθ
Fundamental identities: Even-Odd
sin (-x) = -sin(x)
cos (-x) = cos(x)
tan (-x) = -tan(x)
csc (-x) = -csc(x)
sec (-x) = sec(x)
cot (-x) = -cot(x)
****Cosine is the only one that comes out positive meaning the reciprocal (sec) comes out positive as well****
Fundamental identities: Pythagorean
sin2θ + cos2θ = 1
tan2θ + 1 = sec2θ
1 + cot2θ = csc2θ
Evaluate 0 on the Pi Circle:
sinθ = O
cosθ = 1
tanθ = 0
Evaluate π/6 on the Pi Circle:
sinθ = ½
cosθ = √3/2
tanθ = 1/√3 or √3/3
Evaluate π/4 on the Pi Circle:
sinθ = √2/2
cosθ = √2/2
tanθ = 1
Evaluate π/3 on the Pi Circle:
sinθ = √3/2
cosθ = ½
tanθ = √3
Evaluate π/2 on the Pi Circle:
sinθ = 1
cosθ = 0
tanθ = UND
Evaluate π on the Pi Circle:
sinθ = 0
cosθ = -1
tanθ = 0
Distance Formula-
d = √(x2-x1)2 + (y2-y1)2
Midpoint Formula-
((x1 + x2) /2 , (y1 + y2)/ 2)
