AP Precalc Formula Flashcards

When the graph of f is increasing, the rate of change of f is ______

positive

When the graph of f is concave up, the rate of change of f is _____

increasing

When the graph of f is decreasing, the rate of change of f is _____

negative

When the graph of f is concave down, the rate of change of f is _____

decreasing

Average Rate of Change Formula

y2 - y1 / x2 - x1

For a polynomial of nth degree, what is seen in the table of values:

the nth differences in the output values will be constant

Rule of Complex Zeros

Always come in paris

Multiplicity rules

1st: straight through

2nd: bounce

3rd: wiggle

Symmetry of Even Functions

Symmetrical over y-axis —> f(-x) = f(x)

Symmetry of Odd Functions

Symmetrical over the origin —> f(-x) = -f(x)

Rule of Rational Functions’ Horizontal Asymptotes

BOBO BOTN EATS DC

Rules for Xeros, Holes, Vertical Asymptotes

Zeros: left in numerator

Holes: cancels out numerator and denominator

VAs: left in denominator

Rule for Slant Asymptotes

When the numerator is one degree greater than denominator perform long division

Arithmetic Sequence

a(n) = a(k) + d(n-k)

Geometric Sequence

g(n)=g(k) x r^(n-k)

Rule of Residual Plots

If the residual graph has a pattern, then the regression is not appropriate.

Finding Residual

Actual - predicted

Rule for Invertible Functions

A function must be one-to-one to be invertible, it must have one input value for each output value.

The domain of f becomes the ____ of f(-1)

range

In exponential functions, the ____ are proportional

output values

In logarithmic functions, the ____ are proportional

input values

Pythagorean Identities

sin²x + cos²x = 1

1 +tan²x = sec²x

1 +cot²x = csc²x

sin (A + B) =

sin a cos b + cos a sin b

sin (A - B) =

sin a cos b - cos a sin b

cos (A + B) =

cos a cos b - sin a sin b

cos (A - B) =

cos a cos b + sin a sin b

sin (2x) =

2 sinx cosx

cos (2x) =

cos²x-sin²x

2cos²x-1

1-2sin²x

Converting Polar to Rectangular

x = r cos theta

y = r sin theta

Converting Rectangular to Polar

r = sqr (x²+y²)

theta = arctan (y/x)

Complex Numbers in Polar Form

(r cos theta) + i (r sin theta)