Study Flashcards
What does a^-n also equal?
1/a^n
Also equals 1/a^2
a^-n
(a • b)^2 equals
a^n • b^n
(a/b)^n equals
a^n/b^n
(a/b)^-n equals
(b/a)^n
A^3-B^3 =
(A-B)(A^2+AB+B^2)
(A-B)(A^2+AB+B^2) =
A^3-B^3
A^3+B^3 =
(A+B)(A^2-AB+B^2)
(A+B)(A^2-AB+B^2)
A^3+B^3
7 √20 =
7 √4•5 = 14 √5
Zero product property
If A and B are two expressions, AB=0 iff A=0 or B=0
If A and B are two expressions, AB=0 iff A=0 or B=0
Zero product property
How do you complete the square?
Take b/2 and square it. Then add that to the equation and keep any extra constants on right side
Take b/2 and square it. Then add that to the equation and keep any extra constants on right si
Completing the square
When do you check if a problem has no solutions with a value of x?
When the problem is a rational expression (denominators) or you squared both sides
When a problem has rational expressions (denominators) or you square both sides you
Check the values of x to make sure they don’t have no solution
Domain of inequality
Set of real numbers at which it can be evaluated
Set of real numbers at which an inequality can be evaluated
Domain
Solution set of an inequality
Set of real numbers that make it true
Set of real numbers that make an inequality true
Solution set
A combination of one or more inequalities
Compound inequality
Compound inequality
A combination of one or more inequalities
Distance between two points formula
√(x1-x2)^2 + (y1-y2)^2
Midpoint between two points formula
(x1+x2/2 , y1+y2/2)
√(x1-x2)^2 + (y1-y2)^2
Distance formula between two points
(x1+x2/2 , y1+y2/2)
Midpoint between two points formula
How can you tell if a linear equation is symmetric over the y-axis?
Replace x with -x
Replace x with -x
To tell if a linear equation is symmetric over y-axis
Circle standard equation
(X-h)^2 + (y-k)^2 = r^2
Point slope formula
y-y1 = m(x-x1)
y-y1 = m(x-x1)
Point slope formula
Negative reciprocal slope formula
m1 • m2 = -1
m1 • m2 = -1
Negative reciprocal slope formula
How to tell if a function is even?
Place -x in for x and see if it is the same function
Place -x in for x and see if it is the same function
To tell if a function is even
When is the graph of a function even?
Symmetric over y-axis
If the graph of a function is symmetric over y-axis
Even function
Polynomial with all degrees even
Even function
Polynomial with all odd degrees
Odd function
Polynomial with neither all even nor all odd degrees
Neither even or odd function
Neither even or odd function
Polynomial with neither all even nor all odd degrees
Average rate of change formula
Same as slope formula
Same as slope formula
Average rate of change formula
The graph of a function is neither even nor odd if
Symmetric across x-axis
If a function is symmetric across x-axis
Neither even nor odd function
A function is one to one iff
x=f^-1(y) iff y=f(x)
f^-1(f(x)) =
x
f(f^-1(x)) =
x
Vertex form
f(x)=a(x-h)^2 + k where (h,k) is the vertex
f(x)=a(x-h)^2 + k where (h,k) is the vertex
Vertex form
Properties of a polynomial
Nonnegative exponents and defined on all reals (-∞, ∞)
Nonnegative exponents and defined on all reals (-∞, ∞)
Properties of polynomials
How to find the vertex of a quadratic
(-b/2a, f(-b/2a))
(-b/2a, f(-b/2a))
How to find the vertex of a quadratic
What horizontal asymptote does this have?
f(x) = 5x+2/1-3x
y=-5/3 because equal degrees so determined by leading coefficients
What horizontal asymptote does this have?
2x/x^2 +1
y=0 because bottom is bigger degree
What horizontal asymptote does this have?
3x^2 -1/x+2
None because top degree is bigger
When does a function touch x-axis?
Even multiplicity
When does a function cross the x-axis?
Odd multiplicity
Compound interest formula
A=P(1+r/n)^nt where a is amount, P is principal, r is # of compounds per year, t is time
A=P(1+r/n)^nt
Compound interest formula
Continuously compounded interest formula
A=Pe^rt
A=Pe^rt
Continuously compounded interest formula
Exponential growth and decay formula
A(t)=A(o)e^kt where A(t) is amount after time (t), A(o) is initial amount, k is relative rate of growth, t is time
A(t)=A(o)e^kt
Exponential growth and decay formula
what does the graph of log(a)x where a is any integer look like?
Point at (1,0) and (a,1)
How is 4^3=64 solved?
3=log(4)64
Evaluate log(5)25
log(5)(5^2) = 2
Evaluate log(1/3)9
log(1/3)(3^2) =
log(1/3)((1/3)^-1)^2 = -2
Evaluate log(4)1/2
log(4)(4^-1/2) = -1/2
What does h equal in the half life formula?
h=-ln2/k
h=-ln2/k
H in half life formula
What is always true about the value of k in a half life formula?
It is negative
Always negative in half life formula
k
What is done first here?
3^x - 8 • 3^-x = 2
Multiply both sides by 3^x to get rid of negative exponent
For .7^x<3, what’s the difference between taking the log(.7) of both sides and taking the ln of both sides?
Ln stays on left side and is divided in the end while log operated on only right side
When is an angle in standard position?
When its vertex is at the origin and it’s initial side lies along the positive x-axis
When its vertex is at the origin and it’s initial side lies along the positive x-axis
When an angle is in standard position
The radian measure of an angle θ is
The length of the arc it subtends in the unit circle
Arc length formula
S=rθ where S is arc length and r is radius
S=rθ
Arc length formula
Linear velocity arc length
v=S/t
v=S/t
Linear velocity arc length
Angular velocity arc length
w= θ/t
w= θ/t
Angular velocity arc length
Rotations per minute is handled how?
Multiplied by 2π
Linear and angular speed formula
v=rw
v=rw
Linear and angular speed formula
