calc Flashcards
0
Q
log a (x/y)
A
log a x - log a y
1
Q
log a (xy)
A
log a x + log a y
2
Q
log a (x^r)
A
r log a x (where r is any real number)
3
Q
log a x = y
A
a^y = x
4
Q
cancellation for f(x) = a^x
A
log a (a^x) = x for all REAL x
5
Q
cancellation for f^-1(x) = log a x
A
a^(log a x) = x
6
Q
Laws of exponents
A
a^(x + y) = (a^x)(a^y)
7
Q
3log 2 500 can be broken into
A
3(log500/log2)
8
Q
500 = 2^(t/3) becomes…
A
log 2 500 = t/3
9
Q
4 forms of representation
A
Verbal
Numerical
Graphical
Algebraic
10
Q
Difference Quotient Formula
avg rate of change
A
f(a+h) - f(a)
___________
h
11
Q
Def of function
A
Maps a set of points to another set of points in a one to one relationship
12
Q
logarithmic functions look like
A
log a x = y (low right -> top right)
y-axis is v asymp.
13
Q
Stretch/reflect
A
y = cf(x) : stretch v y = (1/c)f(x) : shrink v
y = f(cx) : shrink h y = f(x/c) : stretch h
y = -f(x) : reflect x-axis y = f(-x) : reflect y-axis
14
Q
change of base formula
A
log a x = ln x / ln a
