exponents, logs, transformations

Question 1

vertical

Answer 1

up: y = a^x + k
down: y = a^x - k

Question 2

horizontal

Answer 2

right: y = a^(x-h)
left: y = a^(x+h)

Question 3

all base exponential functions have

Answer 3

y intercept of (0,1)
Horizontal asymptote of Y = 0

Question 4

reflections

Answer 4

over y axis: change sing of x coordinate

over x axis: change sign of y coordinate

Question 5

inverse of expoenetial function

Answer 5

f(x) = a^x –> loga(x)

Question 6

loga(b^x)

Answer 6

(x)loga(b)

Question 7

turn log equation into exponent

Answer 7

loga(x) = b –> a^b = x

Question 8

change base formula

Answer 8

logb(x) / logb(a)

loga(x) = y
a^y = x
logb(x) = logb(a^y)
y = logb(x)/logb(a)

Question 9

dialations

Answer 9

vertical: y = af(x)
a>1 = stretch
a<1 = compression
Horizontal: y = f(qx)
q>1 = compression
q<1 = stretch

Question 10

vector

Answer 10

(2/3) = (x/y)
Y = a^x-2 + y