College Algebra
Practice Test 3
• This review should prepare you
for the third test in College
Algebra. Read the question,
work out the answer, then
check yourself by clicking the
mouse to see if you’re right.
1. Give the domain and
tell if the set is a
function: {(-1,4), (2,7),
(3,7)}
• -1, 2, 3 ; yes it’s a function
2. Give 3 ordered pairs
that fit
y = x + 100
• Answers may vary: (0, 100) ,
(1, 101), (2, 102), (-1, 99) ,
etc.
3. What is the slope of
3x + 4y = 7
• -3/4
4. What is the y
intercept of
x + 3y = 2 ?
• 2/3
5. What is the xintercept of
-3x + 5y = 9?
• -3
6. What is the distance
between the two points:
(1,4) and (3,8)?
• 2√5 OR ≈4.47
7. Determine whether the three points
are collinear, the vertices of a right
triangle, or neither. (-4,3) (2,5) (-1,-6)
• Vertices of a right triangle
8. What are the
coordinates of the
midpoint of the segment
joining the two points:
(1,4) and (3,8)?
• (2,6)
9. Find the center and radius of the
circle, then graph. A. (x+2)² + y² = 25
B. x² + y² + 8x – 6y + 16 = 0
• A. Center (-2,0) and radius=5
• B. Center(-4,3) and radius=3
10. What is the slope of
the line containing (1,4)
and (3,8)
•2
11. What is the
equation that passes
through (-1,-2) and has a
slope of 3?
• y = 3x + 1
12. What is the
equation of the line that
passes through (1,4) and
is perpendicular to y =
2/3 x + 5?
• y = -3/2 x + 11/2
13. What is the equation
of the vertical line
passing through (1,2)?
•x=1
14. Write the equation of
the line that passes
through (-2,1) and
(-6, -4).
• y = 5/4 x + 7/2
15. Sketch the graph of
3x + 2y = 3
16. Graph y > 3x - 1
17. What type of
equation is
y = 5x + 4?
• Linear
18. Graph y = |x+2| - 3
and give the domain and
range.
• Domain = (-,) Range = [-3,)
19.Graph
y = (x - 2)2 - 1
20. Graph the piecewise
function:
y= -2x if x≤ -1
= x+3 if x> -1
21. What type of
equation is
2
y = x - 5?
• quadratic
22. What is the vertex and axis of
symmetry for y=1/2(x-3)²-1. Then
graph.
• Vertex = (3,-1)
• Axis x=3
23.Find the vertex:
y = x2 - 8x + 16,
and which way would it
open?
• (4,0) , opens up
24. What are the x-intercepts,
y-intercept,vertex and axis of
symmetry for y = x2 - 6x + 5?
•
•
•
•
x-intercepts are 1 and 5
y-intercept is 5
Vertex = (3,-4)
Axis of symmetry is x=3
25. What are the zero’s
of y = x2 + 1 ?
• No solution, it does not cross
the x axis
26. What does it mean about
the graph if there are imaginary
solutions?
• The graph doesn’t cross the x
axis
27.By using parent
graph rules, graph
y = -x2 - 5
28. What is the domain and range for
y=-√(2x-6)+2. Then graph.
• Domain (3,)
• Range (-,2]
29. Divide using
synthetic division:
(2x4 - 3x3 - 6x2 - 8x 3) / (x - 3)
• 2x3 + 3x2 + 3x + 1
30. Divide by synthetic
division:
(x2 - 25) / (x + 5)
• (x - 5)
31. Is -2 a root of y = 2x4+ 6x3
+ 5x - 6? Check using
synthetic division.
• no
32. List the possible rational zeros,
then find the zeros, and write the
factors for y=x³-2x²-13x-10
• ±1,2,5,10
• -1,-2,5
• (x+1)(x+2)(x-5)
33. Describe the end behavior of
the graph and the possible number
of turns: y = x3-x2 - x + 1
• Low to High and 2 possible
turns
34. Describe the end
behavior and number of
turns of y = -5x5 +2x2 -1
• High to Low and have 4 possible
turns
35. 2 is a zero for the following:
y=15x³-34x²+5x+6. Find the other
zeros.
• 3/5 and -1/3
36. If g(x) = x2 -6x+3 ,
find g(-2).
• 19
37. Find f(-3) :
f(x) = x4 - x3+ 4x2 - 8x + 1
• 169
38. Find g(f(x)) if f(x) = x2
- 1 and g(x) = x + 3
• Y = x2 + 2
39.Find f(g(2)) if
f(x) = x2 - 2x and
g(x) = 4x
• 48
40. f(x)=x²-5x and g(x)=x+2
Find (f+g)(x) and (f•g)(x).
• (f+g)(x) = x²-4x+2
• (f•g)(x) = x³-3x²-10x
THE END!!