Math 141 –Review Test 2 (Chapter 3)
No graphing calculator is allowed.
Show all your work for full credit.
3
2
1. Given the function, f ( x ) = 4 x − 23 x + 26 x + 8
a. Give the maximum number of zeros;___________________
b. Use DeScarte’s Rule of signs to determine how many positive
and negative zeros.
c. Find the zeros in the real number system.( Must show your work
for a credit.)
3x 2
2. Given the function, f ( x ) =
(x − 2)(x + 3)
d.
e.
f.
d.
e.
Find the vertical asymptote;________________________
Find the horizontal asymptote.
x intercept;____________________
y intercept;______________________
Draw the graph.
3. Answer the following question for the function,
2
f ( x ) = x ( x + 4 ) ( x − 3)
a. List each real zero;________________________________
.
b. Determine whether the graph crosses or touches the x-axis at each x-intercept
c. Determine the behavior of the graph near each x-intercept.
d. Determine the end behavior.
e. Draw the graph.
4Write an equation for a polynomial the given features.
Degree 5, Zeros of multiplicity 2 at x = 3 and x = 1, and a zero of
multiplicity 1 at x = -3. Vertical intercept at (0, 9)
5. Find the graph that might have the graph shown. Choose the least power
the function can have. (Explain the reason why you choose each step.)
y =1
Solution ( You must show all your work for credits)
1. a. three
b. two or zero possible posite zeros
one negative zero
c. show p and q and p/q possible values.
X= 2, 4 and x = -1/4
2. a. x = -3, 2
b. y = 3
c. zero
d. zero
e. draw the graph
3. a. 0, -4, 3
b at x = 0 and 3 ; corsses, at x = -4 ; touches
c. x = 0; neg.slope, x = -4; pos. slope, x = 3; pos. slope
d. f (x ) = x^4
e. Draw the graph
4. f (x) = (1/3)(x+)(x-3)^2(x-1)^2
5. Draw the graph