y






x


























1. Use the above graph to determine each of the following. Where applicable, use interval notation.
a. the domain
b. the range
c. interval/s on which the function is increasing
d. interval/s on which the function is decreasing
e. the x-intercepts written as ordered pairs
f. the y-intercept written as an ordered pair
g. the relative minimum
h. f(-1)
 x2 1

2. Graph f ( x )    x
5

if x  3
if 3  x  6
if x  6
y






x


























3. Find and simplify the difference quotient f ( x) 
f ( x  h)  f ( x )
, h0
h
a. f ( x)  4 x 2  2 x  7
b. f ( x)  3x  2
c. f ( x) 
3
2x  5
4. Divide using long division. Write the answer in the form q( x) 
r ( x)
.
d ( x)
4x4  4x2  6x
x4
5. Divide using synthetic division. Write the answer in the form q( x) 
(5 x3  6 x 2  3x  11)  ( x  2)
r ( x)
.
d ( x)
6. Use synthetic division and the Remainder Theorem to find the indicated function value.
f ( x)  3x3  7 x 2  2 x  5; f (3)
7. Use synthetic division to divide f ( x)  2 x3  5 x 2  x  2 by x  2 . Use the result to find all zeros of
f .
8. a. List all possible rational zeros. [Problems on page 357 (9-24)
b. Use synthetic division to test the possible rational zeros and find an actual zero.
c. Use the quotient form part (b) to find the remaining zeros of the polynomial function.
f ( x)  2 x3  3x 2  11x  6
9. Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
[Problems on page 357 (25-32)]
n=3
4 and 2i are zeros
f(-1)=-50
10. Find the domain of each rational function. Write in interval notation. ( Section 2.6)
a. f ( x ) 
x 8
x 2  64
b. f ( x ) 
x3
x2  9
c. f ( x ) 
x7
x  10
11. Find the vertical asymptote.
a. f ( x ) 
x 8
x 2  64
b. f ( x ) 
x3
x2  9
c. f ( x ) 
x7
x  10
12. Find the horizontal asymptotes.
x4
x  x6
a. f ( x) 
2
b. f ( x) 
13x3  6
3x 2 5
c. f ( x) 
5 x3  2 x 2  5
3x3  2
13. Find the slant asymptote if there is one.
x2  x  1
a. f ( x) 
x 1
b. f ( x) 
x3  x 2  8 x  6
5x  6
14. Find the domain, the intercepts, and the asymptotes, and use them to sketch the graph of
f ( x) 
3x
x 1
y






x


























15. Solve the polynomial inequality f ( x)  x3  7 x 2  x  7  0 . Graph the solution set on a real
number line, and express the solution in interval notation.
16. Solve the rational inequality
x4
 0 and graph the solution set on a real number line. Express the
x 3
solution set in interval notation.
17. Showing each of the four steps, find an equation for f 1 ( x).
a. f ( x)  x  5
b. f ( x)  ( x  2) 3
c. f ( x) 
3
x
18. Use the graph of f to draw the graph of its inverse function.
y






x





















19. Write each equation in its equivalent exponential form. (section 3.2)
a. logb38 = x
b. 8 = log2w
20. Write each equation in its equivalent logarithmic form.
a. 25 = 32
b. b3 =343





21. Find the domain of each logarithmic function. Write in interval notation.
a. f ( x)  log(7  x)
b. f ( x)  ln( x  6)2
c. f ( x)  log( x  19)
22. Evaluate and simplify each expression without using a calculator. (page 438)
a. log4 = 16
b. log7 = 1
c. ln 1
d. log446
e. log 100
23. Graph f(x) = 2x. Plot points. Then using transformations graph g(x)= 2x +3
24. Approximate each number using a calculator.
a. 3-5.7
b. e4.5
25. Using you graphing calculator, find each of the following rounded to three decimal places for the
function f ( x)  2 x3  5x 2  x  1 .
a. the real zeros
b. the relative maximum
c. the relative minimum
d. f(-6)
 r
26. Use the compound interest formulas A  P  1  
 n
nt
or A  Pe rt to solve. Round answers to the
nearest cent.
Find the accumulated value of an investment of $15,000 for 4 years at an interest rate of 5.5% if the
money is
a. compounded monthly
b. compounded continuously