Math 131 Exam 1 Review for Week in Review
1. Find the domain of each function.
a)
f ( x )  ln( x 2 )
d)
f ( x) 
f ( x )  2 ln x
b)
x2  5x  6
e)
f ( x) 
f ( x) 
c)
1
ln( x  3)
1
x2  5x  6
2. Find the range of each function.
a)
f ( x )  5e  x  6
c)
f ( x)  x 2  9
f ( x )  3 ln x  4
b)
f ( x) 
d)
1
x 1
2
3. Write the basic function and the transformations which result in the given function.
a)
f ( x )  3e  ( x  2 )
c)
f ( x )  4 ( x  5) 3  8
b)
f ( x )   5 e x 1  7
d)
f ( x )  ln( 2  x )
4. Find the inverse function to the given function. Give the domain and range of the function and its
inverse.
a)
f ( x )  3e 4 x  2
c)
f ( x )  2 x 2  8 restricted to (  ,0 ]
b)
f ( x )  2 x 2  8 restricted to [ 0,  )
d)
f ( x) 
ln x
5. Find f  g  x  and g  f  x  .
a)
f ( x )  3( 2 x )
g ( x )  ln x
b)
f ( x)  x 2  1
g ( x) 
x
6. A culture grew exponentially so that at t=0 hours there were 15 g and at t=5 hours there were 20 g.
a) Write the formula for the weight at t hours.
b) Find the weights at t=0, at t= 15 and at t=17.
c) Write the formula in base e and find the continuous growth rate.
7. Solve each equation for x.
a)
9 x  3 x  2  28  0
b)
e 2 x  5e x  150
8. A principle of $20,000 was invested at the annual interest rate of 3% compounded continuously.
Find the amount in the account after 20 years.
9. The half life of a certain drug in the body is two days. If 16 mg are taken on day 0, in how many days
will the amount remaining be 1 mg?
10. Evaluate lim f ( x ),
xa 
a)
c)
f ( x) 
f ( x) 
x2  x  6
2x2  4x
x2  2x  3
( x  1) 3
lim f ( x ) Does lim f ( x ) exist?
xa 
a2
x a
b)
f ( x) 
a  1 d )
f ( x) 
x2  x  6
2x2  4x
sin 3 x
x
a0
a0
11. Find all discontinuities of f(x) if any.
f ( x) 
a)
x 1
 x2  1
 2
 x  2x  3
f ( x)  

0


2
b)
x2  2x  3
x  1 and
x  3
1  x or
x  3
12. Find the value of A which makes f(x) continuous for all x.
 Ax  7
f ( x)   2
x  A
13 a )
d)
lim
x
lim
x

2 x
3e x  5
4  ex
x  5 x3
x  
f) lim
x2
x 4  10
x2  2x 
b)
e)
lim e
x
lim
x
x2  4x

1
sin  
x
c)
4 x 3  12 x 2  1
25  3 x 3
lim
x  
8 x 5  4 x 4  27
3x2  2 x