Math 119 – Practice Test 3
1.
Name_______________________________
Use the graph to find f (2).
[A] -2
[B] -1
[C] 0
[D] 1
[E] none of these
Use the following graph for #2-5
2.
Based on the end behavior shown in the graph, the degree of the polynomial must be…
[A]
positive
[B]
negative
[C]
even [D]
odd
[E] none of the these
3.
Based on the end behavior shown in the graph, the leading coefficient must be…
[A]
positive
[B]
negative
[C]
even [D]
odd
[E] none of the these
4.
The multiplicity of the zero x  2 must be…
[A]
positive
[B]
negative
[C]
even
[D]
odd
f (2) =______
[A]
8
[B]
5.
6.
7.
8.
3
[C]
[E] none of the these
0
[D]
-8
[E]
-16
What is the slope of a vertical line?
[A]
positive
[B]
negative
[C]
zero
[D]
undefined
Identify the domain of the square root function
[A]
[B]
[C]
0, 
0, 
 , 
[D]
Identify the equation of the vertical line through the point  5,2
[A]
[B]
[C] y  5
[D]
x  5
x2
 ,0
y2
1.
Determine the quadrant(s) in which ( x, y ) is located so that the conditions are satisfied.
x  2, y  0
a.
b.
x  0 and y  0
c.
x  0 and  y  0
2.
Find the x and y intercepts of the graph of the function shown. List them as ordered pairs.
x-int(s):_________________________________________
y-int(s):_________________________________________
3.
4.
Find the slope-intercept form of the equation of the line passing through the points:
a.
(1,3) and (2,8)
b.
 1
1 5
 2,  and  , 
 2
2 4
Refer to the graph of the line shown.
a.
Identify the slope and the y-intercept (pay attention to the scale on the x-axis)
Slope = __________; y-int.__________
b.
Write the slope-intercept form of the equation of the line shown in the graph.
5.
Write the equation of the line that is parallel to the line 7 x  4 y  12 and goes through the
point (0, 2) .
6.
Write the equation of the line passes through (3,5) and is perpendicular to the line whose slope
is  12 .
7.
a.
b.
8.
x
f(x)
2 x  2 if x  1
Graph the function f ( x)  
2 x  3 if x  1
Find the domain and the range of f (x) .
Complete the table of values for the function
 1 x2
if
x  5

f ( x)   3 x  5
if  5  x  2
3
2
 x  x  x if
2 x

-6
-2
1/2
2
3
9.
a.
Find the range of the piecewise function shown in the graph above (assuming that the
lines extend forever past what is shown)
b.
Determine the interval(s) over which the graph of the function above is increasing and
decreasing.
Increasing:___________________
Decraseing:__________________
10.
Write an equation for the function that has the shape of the absolute value function but has been
moved 1 unit to the left, reflected across the x-axis, then shifted 9 units up. (You don’t have to
sketch the graph.)
11.
Find the vertex and x-intercepts, and use them to sketch the graph of the function.
g ( x)  x 2  6 x  8
12.
13.
14.
15.
a.
Write the equation of the horizontal line that passes through the point (-1,3).
b.
What is the slope of a vertical line?
a.
Find the zero(s) of the function g ( x) 
b.
Find the zero(s) of the function h( x)  x 3  4 x 2  25x  100
x5
.
3x  2
True or False? (Write out the whole word—not just T or F.)
a.
A polynomial function of degree 8 can have at most 9 turning points. __________
b.
The graph of g ( x)  x 6  5 is a U-shape shifted up 5 units from (0, 0) .__________
c.
1
The parabola described by y   x 2  3x  1 opens upward._________
4
Describe (in words) the transformation from a common function and then sketch the graph.
Be sure to say what the common function is. Put only your final answer on the grid below,
labeling three points.
g ( x)   x  2
16.
Describe (in words) the transformation from a common function and then sketch the graph.
Be sure to say what the common function is. Put only your final answer on the grid below,
labeling three points.
h( x)  ( x  1)3  3
17.
Determine the end behavior of f ( x)  7 x3  4 x  19 .
18.
Determine the end behavior for g ( x) 
19.
Find a polynomial function that has the given zeros: 0,-2,-3.
20.
Use the function f ( x)  x( x  2) 2 ( x  2)
1 8
x  5 x 7  43x 6  x 4  493x3  173 .
111
a. Find the x-intercepts (zeros) of f (x)
b. Give the multiplicity of each zero and use it to describe the graph’s behavior at that zero.(i.e
does the graph cross over the x-axis or just touch without crossing?)
Zero
Multiplicity
Description of the graph’s behavior at the zero
c. Simplify f (x) . (Multiply and collect like terms)
d. Use the leading coefficient test to determine the end behavior of f (x) .
e. Complete the table of values for f  x  .
x
f(x)
-3
75
-2
-1
0
1
2
3
f. Use the zeros, the multiplicity, the end behavior and the table of values to sketch the graph of
f  x .
Note: You do not need to plot the point (-3, 75).