Sec. 4.1-4.3Sec. 4.1-4.3

Write the expression using logs:Write the expression using logs:

2x=7.2

log27.2=x

If every horizontal line intersects the graph of a function f at no more than one point, the f is a(n) ____________ function.

one-to-one

Find the inverse:Find the inverse:

f(x) = 2x + 6

1 1( ) 3

2f x x

Write the expression in exponential Write the expression in exponential form:form:

log2M = 1.3

21.3 = M

If the graph of every exponential function f(x) =

ax, a>0, a not = 1, is decreasing, then a must be

less than _________.

1

Graph f(x)=4x

(0,1) (1,4) (-1,1/4)(0,1) (1,4) (-1,1/4)

If f -1 denotes the inverse of a function f, then the graphs of f and f -1 are symmetric

with respect to the line ___________.

y = x

Find the inverse:Find the inverse:

{(1,2),(2,8),(3,18),(4,32)}

{(2,1),(8,2),(18,3),(32,4)}

Graph f(x)=log4x

(1,0) (4,1) (1/4,-1)(1,0) (4,1) (1/4,-1)

What is the asymptote of the graph f(x)=5+e-x?

y = 5

Solve:Solve:

(1/5)2-x = 25

x = 4

What is the domain of the function f(x)=3x+2?

( , )

What is the domain

? 1

( ) ln1

f xx

( 1, )

Find the exact value Find the exact value (without using a calculator)(without using a calculator)

2log 4

4

What is the domain of the function?

( ) 2 log( 3)f x x

( 3, )

Determine if the two functions are Determine if the two functions are inverses of each other:inverses of each other:

2( )

3

2 3( )

f xx

xg x

x

nono

2

( ( ))1 3

2 12( ( ))

3

xf g x

x

xg f x

x x

Solve:Solve:

3log 243 2 1x

x = 2

What is the asymptote

of the function

h(x) = 3 + log(x + 2)?

x = -2

What is the domain of the function

F(x) = log(2-x)?

( ,2)

Determine if the two functions are Determine if the two functions are inverses of each other:inverses of each other:

2 3( )

4

4 3( )

2

xf x

x

xg x

x

yesyes

f(g(x)) = g(f(x)) =x