Memory #1 Calc

Function

A mathematical relation that maps a set on input values to a set of output vaues such that each input value has exactly one output value.

Domain

A set of input values of a function, represented by the independent variable

Range

A set of output values of a function, represented by the dependent variable

What is slope also known as.

Average rate of change

How does the function behave if it is decreasing

If a<b, then function f is decreasing so long as f(a) > f(b)

How does a function behave if it is increasing.

If a<b, then function f is increasing so long as f(a)<f(b)

When does a function have a relative minimum

A function has a relative minimum if at some point, the graph of the function changes from decreasing to increasing.

When does a function have a relative maximum

A function has a relative maximum if at some point, the graph of the function changes from increasing to decreasing

When does a polynomial have an absolute maximum

If polynomial p has an even degree leading term and has a leading coefficient that is negative we can say there is an absolute maximum that exists on function p

When does a polynomial have an absolute minimum

If polynomial p has an even degree leading term and has a leading coeffitient that is positive, we can say there is an absolute minimum that exists on function p

Where do relative maximums and minimums need to be

between 2 real zeroes of a polynomial

Concave down

If the average rate of change over an interval is decreasing

Concave up

If the average rate of change over an interval is increasing

Point of inflection

When a function changes from concave down to concave up or vice versa.

Rate of change of a linear function

Constant

Quadratic’s rate of change

The rate of change of a quadratic funtion’s rate of change is constant

Reference angle

The distance from an angle to the x-axis. Always positive

What is the equation for radian conversions

pi/180

What is the tan quotient identity

tanθ = sinθ/cosθ

What is the cotangent quotient identity

cotθ=cosθ/sinθ

How many radians is 1 revolution

2pi

arc length equation

s=rθ

Area of a sector equation

A=1/2r²θ

Linear speed equation

v=s/t

Angular speed equation

ω=θ/t

What are trigonometric function(s) are even

cosine (sec)

What are trigonometric function(s) are odd

Sine, Tangent (Cosecant, Cotangent)

sin(u+v) equation

sin(u)cos(v)+cos(u)sin(v)

sin(u-v) equation

sin(u)cos(v)-cos(u)sin(v)

cos(u-v) equation

cos(u)cos(v)+sin(u)sin(v)

cos(u+v) equation

cos(u)cos(v)-sin(u)sin(v)

tan(u+v) equation

(tan(u)+tan(v))/(1-tan(u)tan(v))

tan(u-v) equation

(tan(u)-tan(v))/(1+tan(u)tan(v))

Periodic relationship

If, as input values increase the output values demonstrate a repeating pattern over successive equal length intervals.

Cycle

One set or repeating values in a periodic function

Period

How long until the pattern repeats.

What is found in every periodic function

All characteristics found in one period of the function will be in every period of the function

Amplitude

The distance from midline to top/bottom

Frequency

How many cycles in 1 unit of time

Even functions

If f(-x)=f(x)

Odd functions

If f(-x)=-f(x)

y=sin(x)

Here it is

y=cos(x)

Here it is

y=tan(x)

Here it is

y=csc(x)

Here it is

y=sec(x)

Here it is

y=cot(x)

Here it is