Name:
Period:
College Algebra: Ch.1-2.2 Graphs and Functions
MU
You must show all your work for full credit. Ask me to clarify any questions you may have. No Calculators.
In problems 1 - 5, choose the one alternative that best completes the statement or answers the question. Supporting
work/reasoning must be shown in order to receive credit for your answer.
1. List the intercepts for the graph of the equation
A) (-16, 0), (0, -9), (0, 9), (16, 0)
B) (-4, 0), (0, -3), (0, 3), (4, 0)
C) (-9, 0), (-16, 0), (16, 0), (9, 0)
D) (-3, 0), (-4, 0), (4, 0), (3, 0)
E) none of the above
9x 2  16 y 2  144
2. The general form of the equation of the circle with radius =
A) x 2  y 2  12x  12 y  67  0
1. ______(+2)
5 and center = (-6, -6).
2. ______(+2)
B) x 2  y 2  12x  12 y  67  0
C) x 2  y 2  12x  12 y  41  0
D) x 2  y 2  12x  12 y  41  0
E) none of the above
3. The simplified form of
4 24  3 32  2 50
2
A) 5 6  22 2
B) 4 6  2
C) 8 6  2 2
D) 4 6  12 2
E) none of the above
4. Determine f(2x - 1) when f ( x)  3x 2  2 x  7
A)
B)
C)
D)
3. ______(+2)
4. ______(+2)
12x 2  8x  6
4 x 2  8x  6
12 x 2  8x  12
12x 2  8x  5
E) none of the above
5. The Domain of K ( x) 
x
32 x  18
A) All Real Numbers, except x = 0
3
B) All Real Numbers, except 
4
C) All Real Numbers
3
D) All Real Numbers, except
4
E) none of the above
2
5. ______(+2)
6. Find all points (x, y) with x-coordinate of -2 that are 8 5 units away from the point (6, -5).
6. __________________(+5)
7. If (6, -2) is the endpoint of a line segment and (-4, 5) is its midpoint, determine the other endpoint. Justify work.
7. _________________ (+3)
Find the coordinates (x, y) of all intercepts.
8. 9 x  4 y  78
9.
3x 2  y  12 x  96
8. ______________________(+4)
9. ______________________(+4)
10. Determine the equation of the line perpendicular to 7 x  3 y  5 containing the point (-4, 3) and give equation in
a) slope-intercept, b) point-slope, and c) general forms.
10. a) _______________________ (+3)
b) __________________________(+1)
c) __________________________ (+1)
11. Determine the a) standard form and b) general form of the equation of a circle with center (1, -3) that includes the
point (5, -5).
11. a) ______________________________ (+3)
b) _________________________________ (+2)
12. Find the equation of the line in slope-intercept form that connects the centers of the two given circles.
x 2  y 2  4 x  8 y  10  0
x 2  y 2  18 x  18 y  59  0
and
12. ______________________ (+5)
13. Determine the general equation of the circle shown in the figure below if the midpoint of line segment
L is the center of the circle.
13. ______________________________ (+5)
14. For f ( x) 
2x  1
, determine f(-2).
x 2  4x  1
14. __________________ (+2)
15. For f ( x)  2 x 2  3x  1 and g ( x)  3x 2  5 , determine the following…simplify fully.
a) f  g
b) f  g
a) __________________ (+2)
c)
b) __________________ (+2)
g ( x  h)  g ( x )
h
c) __________________ (+5)
16. Find the domain of each function.
2
x 1
a) f ( x)  2
b) Z ( x) 
 6x
2
3
12 x  8x  15
c)
g ( x) 
3x 2
2x  3
16. a)___________________ (+3)
b)__________________________ (+3)
6 x 2  42 x  12
17. For f ( x) 
, determine
x 1
a) the coordinates (x, y) of all intercepts
a) ______________________(+3)
c)____________________(+3)
b) value(s) of x to make f(x) = -28
b) ______________________(+5)