Cold Info PreCal Flashcards
Absolute Rate of Change Equation
f(b) - f(a) / b - a
Secant Line
a line formed between two points using the average rate of change
Increasing Function ROC
positive ROC
Decreasing Function ROC
negative ROC
Concave Up ROC
ROC increasing
Concave Down ROC
ROC decreasing
Point of Inflection
rate of change changes from increasing to decreasing or vice versa
Odd Degree of Inflection - Ends
opposites
Even Degree of Inflection - Ends
the same
Positive Leading Coefficient
positive at end
Negative Leading Coefficient
negative at end
Polynomial Function Bases Equation
a( f[ b(x - h) ]) + k
a = vertical dilation
b = horizontal dilation of 1/b
h = horizontal translation of -h
k = vertical dilation
General Form of Rational Functions
f(x) = ax … / bx …
Rational Functions - Vertical Asymptotes
when a factor in the denominator does not “cancel out” with factors in the numerator
Rational Functions - Horizontal Asymptotes
function degrees
n<m – y=0
n=m – y=a/b
n>m – slant
Rational Functions - Slant
n>m
if the degree of the numerator is larger than the denominator, use long decision to find equation of the slant
Rational Functions - Holes
occur when a common factor “cancels out” after simplifying
locate the hole by evaluating the simplified expression at the x-value of the hole
Base Linear Function
f(x) = mx + b
Base Exponential Function
a(b)^[x-h] + k
