GRAPHING LOGARITHMIC FUNCTIONS Flashcards
(18 cards)
Rules of Logarithms: BASIC
logb(1) = 0
logb(b) = 0
log10(b) = logb(b) = 0
COMMON LOGARITHM
ln (1)=0
ln(e)=1
ln(ex)=x
NATURAL LOGARITHM
In the natural logarithm, what does “e” stand for?
EULER’S NUMBER
Why is Euler’s number also called “the natural number”?
Because it also appears in applications like compound interest, growth and decay, physics cooling and heating, probabilities, chemical reactions and so on.
logb(mn) = logbm + logbn
PRODUCT RULE
logb(m/n) = logbm - logbn
DIVISION RULE
logb(mn) = n logbm
EXPONENTIAL RULE
logbm = logam/logab
CHANGE OF BASE RULE
logb(a) = 1/loga(b)
BASE SWITCH RULE
Where: b >0, b≠1, and m and n are positive real numbers
What is the inverse of bc?
a
What is the inverse of logba
c
What is the simplest logarithmic function?
f(x) = log2x
If the exponential graph’s FUNCTION INCREASES AS X INCREASES from left to right and its domain = (0, ∞), what is the value of the base?
GREATER THAN 1
If the exponential graph LIES TO THE RIGHT OF THE Y-AXIS and its range = set of all real numbers, what is the value of the base?
COULD BE: GREATER THAN 1OR LESS THAN 1 BUT GREATER THAN 0
If the exponential graph has a VERTICAL ASYMPTOTE X=0 meaning the x value gets closer to 0 as y approaches -∞, what is the value of the base?
COULD BE: GREATER THAN 1 OR LESS THAN 1 BUT GREATER THAN 0
In the logarithmic function f(x)=Alogb(x-h)+k, what are: h, k, x, and A?
h: translation along the horizontal
k: translation along the vertical
x = h is the vertical asymptote
A: expansion (if A >1) or contraction (if A < 1)
What happens if the value of A is negative?
Graph is flipped along the x-axis
