PRO Algebra Flashcards
x^m * x^n
x^(m+n)
(x^m)^n
x^(m*n)
x^0
1
x^-m
1/x^m
x^m / x^n
x^(m-n)
What is the midpoint formula?
(x1+x2)/2, (y1+y2)/2
What is the distance formula?
d=Square root of (x2-x1)^2 + (y2-y1)^2
What is the quadratic formula?
-b +/- the square root of b^2 minus 4ac all over 2a
(a^3 + b^3)
(a+b)(a^2-ab+b^2)
(a^3 - b^3)
(a-b)(a^2+ab+b^2)
a^2-b^2
(a-b)(a+b)
a^3+3a^2b+3ab^2+b^3
(a+b)^3
a^3-3a^2b+3ab^2-b^3
(a-b)^3
What is the HA if the degree of the numerator is less than the degree of the denominator?
0
What is the HA if the degree of the numerator is greater than the degree of the denominator?
DNE
What is the HA if the degree of the numerator is equal to the degree of the denominator?
Ratio of leading coefficients
What kind of symmetry exists if f(-x) is equal to f(x)?
Y-axis
What kind of symmetry exists if f(-x) is equal to -f(x)?
Origin
How do you find y-intercepts?
x=0
How do you find x-intercepts?
y=0, only pay attention to numerator
How do you find VA’s?
When the numerator equals a number, but the denominator is equal to 0
How do you find slant asymptotes and how do you know if there will be one?
If the degree of the numerator is one more than the degree of the denominator, you can find a slant asymptote by dividing the numerator by the denominator (the remainder does not count)
What is Ln a + Ln b?
Ln ab
What is Ln a - Ln b?
Ln a/b
Simplify Ln a^P
P times Ln a
What is another form of logb(x)=C?
b^c=x
Change logb(x) to natural logs
Ln x / Ln b
What is the formula for continuously compounding interest?
P*e^rt
What is the formula for interest compounded less than continuously?
P * (1+r/n)^nt
Y is directly proportional to z
Y=kx
Y is inversely proportional to x
Y=k/x
Y is jointly proportional to x and n
Y=kxn
What is the formula for a parabola?
Ax^2+Dx+Ey=0
or y=ax^2+bx+c
change to y=a(x-h)^2+k, where vertex is (h,k) and 1/4a is the distance between the vertex and the focus or directrix
In the regular form the x of the vertex is -b/2a
What is the formula for a circle?
x^2+y^2+Dx+Ey+F
or (x-h)^2+(y-k)^2=r^2
(h,k) is center, r is radius
What is the formula for a ellipse?
Ax^2+Cy^2+Dx+Ey+F=0
Wide:(x-h)^2/a^2+(y-k)^2/b^2=1
Tall:(y-k)^2/a^2+(x-h)^2/b^2=1
The center is at (h,k), the a is distance right, the b is distance left, and the foci is c (a^2-c^2=b^2) units on the sides of the center
What is the formula for a hyperbola?
Ax^2-Cy^2+Dx+Ey+F=0 Cupping y-axis:(x-h)^2/a^2-(y-k)^2/b^2=1 Cupping x-axis:(y-k)^2/a^2-(x-h)^2/b^2=1 Center:(h,k) Vertex is a from center Foci are c from center (c^2-a^2=b^2) Asymptotes are +/- b/a(x-h)+k or +/- a/b(x-h)+k
How do you find the inverse of a function?
Switch the x and y
What is the relationship between the domain and range of f^-1 related to f?
They switch
If f and g are inverses what are f(g(x)) and g(f(x))?
x
How do the graphs of f and its inverse relate?
The inverse is a reflection over y=x
What is the requirement for a function to have an inverse?
It must be one to one, (passing both the vertical and horizontal line tests)
What is i^2?
-1
For an imaginary number a+bi, what is the real part and what is the imaginary part?
a,b
What is the limit on “log”ing numbers?
You cannot log 0 or a negative number
x^m/n
The n root of x^m
What is the average rate of change of a function between two x-values?
The slope of the line connecting them, or Y2-Y1 over X2-X1
What is gof?
The function f inserted as the x in function g
