Study Flashcards by Conor Keegan

What does a^-n also equal?

1/a^n

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Also equals 1/a^2

a^-n

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(a • b)^2 equals

a^n • b^n

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(a/b)^n equals

a^n/b^n

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(a/b)^-n equals

(b/a)^n

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A^3-B^3 =

(A-B)(A^2+AB+B^2)

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(A-B)(A^2+AB+B^2) =

A^3-B^3

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A^3+B^3 =

(A+B)(A^2-AB+B^2)

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(A+B)(A^2-AB+B^2)

A^3+B^3

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7 √20 =

7 √4•5 = 14 √5

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Zero product property

If A and B are two expressions, AB=0 iff A=0 or B=0

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If A and B are two expressions, AB=0 iff A=0 or B=0

Zero product property

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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

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Take b/2 and square it. Then add that to the equation and keep any extra constants on right si

Completing the square

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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

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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

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Domain of inequality

Set of real numbers at which it can be evaluated

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Set of real numbers at which an inequality can be evaluated

Domain

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Solution set of an inequality

Set of real numbers that make it true

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Set of real numbers that make an inequality true

Solution set

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A combination of one or more inequalities

Compound inequality

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Compound inequality

A combination of one or more inequalities

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Distance between two points formula

√(x1-x2)^2 + (y1-y2)^2

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Midpoint between two points formula

(x1+x2/2 , y1+y2/2)

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√(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

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)

Point slope formula

Negative reciprocal slope formula

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

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

Polynomial with neither all even nor all odd degrees

Average rate of change 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)) =

f(f^-1(x)) =

Vertex form

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 (-∞, ∞)

Properties of polynomials

How to find the vertex of a quadratic

(-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

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 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

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 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

Linear velocity arc length

Angular velocity arc length

w= θ/t

Angular velocity arc length

Rotations per minute is handled how?

Multiplied by 2π

Linear and angular speed formula

v=rw

Linear and angular speed formula