Lecture Notes Flashcards

Flashcards with vocabulary terms and definitions extracted from lecture notes.

x value

Input value; independent variable

y value

Output value; dependent variable

Increasing functions

Input values increasing and output values increasing

Decreasing functions

Input values increasing and output values decreasing

Concave up

Up like a cup

Concave down = down like a frown

Down like a frown

Average rate of change

Slope

Rate of change of the average rates of change of a linear function

Zero

Rate of change of the average rates of change of a quadratic function

Always constant (the same)

Relative maximum

When a function switches from increasing to decreasing

Absolute maximum/minimum

The greatest or least of the relative minimums & maximums. DNE when graph has arrows on ends.

Multiplicity

When a factor of a function is repeated (found in exponent)

Zeros

Can be complex zeros (non real) but there must be an even amount because if a+bi is a zero so is a-bi

Even Degree

y-axis symmetry; if (a,b) is on the graph, (a,b) is on the graph

Odd Degree

Origin symmetry; if (a,b) is on f, (a,b) is on f

End behavior

As x goes to infinity what y does go to; As x goes to negative infinity what does y go to

Rational function

g(x) cannot equal zero

HA

Horizontal Asymptote

Zeros

Factors of the numerator (reduced form)

Holes

Factors of the denominator & numerator (cancel out)

Vertical Asymptotes

Can never be crossed

1.13

Linear = 1st diffrence the same

1.13

Quadratic = 2nd diffrence the same

Writing sentence: on average, time, subject, increses/ decreases, label answer

Stat edit > Plugin numbers -find regression with best r value

Arithmetic Sequence

Common diffrence, constant rate of change

Geometric Sequence

Exponental/proportonal, common ratio

Residuals

Actual - predicted

Composition of functions

Take one function and substitute into another function

inverse

A function has an inverse or is invertible if it can pass the horizontal line test

Scales

log, c = a -> b^a = c, b > 0 and b != 1

Logarithmic Function

loga B = loga C Then B=C

Periodic relationship

Periodic relationship = repeating pattern over successive equal-length interval

period

Cycle length

arc length

s = r * theta

Tangent Function

tan = sin/cos

Unit Circle

sin = y/r; cos = x/r; tan = y/x

(x, y) Cartesian Conversion

x = r * cos(theta); y = r * sin(theta)

Midline

y = a * cos(b(theta - c)) + d

Tangent

Opposite of cosine

trig values

arcsin quadrent I, -I

arclos

arcsin quadrent I, I

arctan

arcsin quadrent I.-I

3.11

Cosecant csc x= 1/Sin x

3.11

Secant Sec x= 1/COS x

3.11

cotangent cot x= 1/tan x

Polar to rectangular

x=rcos 0, y= rsin 0

Rectangular to polar

r = sqrt(x^2 + y^2); 0 = tan^-1(y/x)