39)
An ellipse and a hyperbola; four points
39)
40)
A parabola and a hyperbola; three points
40)
Provide an appropriate response.
41)
Describe the graph of the solution set of the following inequality:
y > x2– 10
41)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
42)
–8x2+ 10y2=36
x – 9y = – 1
42)
Provide an appropriate response.
43)
There are some fundamental differences between graphing a hyperbola centered at the
origin and graphing an ellipse centered at the origin. What are these differences?
43)
44)
Describe the graph of the solution set of the following inequality:
x > y2+ 5
44)
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of
intersection of the two graphs is as given. Make a sketch satisfying these conditions.
45)
A parabola and a hyperbola; four points
45)
46)
A line and a parabola; one point
46)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
47)
–5x2– y2=1
9x2+ 4y2=64
47)
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of
intersection of the two graphs is as given. Make a sketch satisfying these conditions.
48)
A circle and an ellipse; four points
48)
49)
A parabola and a circle; three points
49)
Provide an appropriate response.
50)
Describe the graph of the solution set of the following inequality:
y > – x2– 7
50)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle.
51)
5y2– 2x =1
51)
A)
hyperbola
B)
circle
C)
parabola
D)
ellipse
Graph the function defined by a radical expression.
26
52)
f(x) = – 25 – x2
52)
A)
B)
C)
D)
Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
53)
x2– y2=36
53)
A)
Ellipse
B)
Circle
C)
Parabola
D)
Hyperbola
Graph the nonlinear inequality with restrictions.
54)
4x2+25y2100, x 0, y 0
54)
A)
B)
C)
D)
28
Solve the system by the substitution method.
55)
y = 3x2+ 6x
y =x2– 4x + 12
55)
A)
{(2, 0), (3, 45)}
B)
{(2, 0), (–3, 9)}
C)
{(1, 9), (–6, 72)}
D)
{(–2, 0), (–3, 9)}
56)
y = x2– 14x + 49
x + y =19
56)
A)
{(3, 22), (10, 9)}
B)
{(7, 12)}
C)
{(–3, 22), (–10, 29)}
D)
{(3, 16), (10, 9)}
Decide whether the statement is true or false.
57)
The circle with equation (x + 4)2+ (y – 4)2=64 has center at (4, –4).
57)
A)
True
B)
False
Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle.
58)
36y2=144 + 4x2
58)
A)
ellipse
B)
parabola
C)
hyperbola
D)
circle
Graph the system of inequalities.
29
59)
2x + y 4
x – 1 0
59)
A)
B)
C)
D)
30
Provide an appropriate response.
60)
For the reciprocal function defined by f(x) =1
x, is the only real number not in the
domain.
60)
A)
–1
B)
1
C)
1
2
D)
0
Solve the system by the elimination method or a combination of the elimination and substitution methods.
61)
x2+ y2= 85
x2– y2= 13
61)
A)
{(7, –6), (7, 6)}
B)
{(7, 6), (6, 7), (–7, –6), (–6, –7)}
C)
{(–7, –6), (–6, –7)}
D)
{(7, 6), (–7, 6), (7, –6), (–7, –6)}
Graph the inequality.
62)
y2– 16 –4x2
62)
A)
B)
31
C)
D)
Find the center and radius of the circle whose equation is given.
63)
x2+ y2+ 10x – 10y + 50 =64
63)
A)
center: (–5, 5); radius: 8
B)
center: (5, –5); radius: 8
C)
center: (–5, 5); radius: 64
D)
center: (5, –5); radius: 64
32
The circle or ellipse shown in the calculator–generated graph was created using function mode with a square viewing
window. What are the two functions y1 and y2 that were used to obtain the graph whose equation is given?
64)
x2
16 +y2
25 = 1
64)
A)
y1= 5 1 –x2
16 , y2= – 51 –x2
16
B)
y1= 5 1 –x2
4, y2= – 51 –x2
4
C)
y1= 5 1 +x2
16 , y2= – 51 +x2
16
D)
y1= 5 1 –x
4, y2= – 51 –x
4
The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one
of the solutions. Find the other solution.
65)
y = – 1
2x2
x + y = – 4
65)
A)
(–8, 4)
B)
(4, –6)
C)
(4, –8)
D)
(4, 8)
Solve the problem by using a nonlinear system.
66)
The area of a rectangular rug is 198 ft2 and its perimeter is 58 feet. Find the dimensions of the rug.
66)
A)
12 ft by 18 ft
B)
11 ft by 18 ft
C)
11 ft by 17 ft
D)
12 ft by 17 ft
Graph the ellipse.
67)
x2
49 +y2
9= 1
67)
A)
B)
C)
D)
Graph the system of inequalities.
68)
y –x2
y x + 1
y –5
x –4
68)
A)
B)
C)
D)
69)
2x + y 4
x – 1 0
69)
A)
B)
C)
D)
36
Evaluate the expression.
70)
[[–12.2]]
70)
A)
–13
B)
–12
C)
–11
D)
–3
The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one
of the solutions. Find the other solution.
71)
y = – 1
3x2+ 5
x – y = 1
71)
A)
(–5, –8)
B)
(–6, –7)
C)
(6, 7)
D)
(–7, –6)
Graph the function.
72)
f(x) =7x– 6
72)
37
A)
B)
C)
D)
Graph the system of inequalities.
73)
3x – 2y –6
x – 1 < 0
73)
38
A)
B)
C)
D)
Graph the hyperbola with center shifted away from the origin.
74)
(x – 2)2
25 –(y – 4)2
16 = 1
74)
39
A)
B)
C)
D)
Graph the function defined by a radical expression.
75)
f(x) =49 – x2
75)