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.
115)
y = – x2
x + y = – 2
115)
A)
(–2, 4)
B)
(2, –4)
C)
(1, 1)
D)
(–4, 2)
Graph the function. Give the domain and range.
116)
f(x) =x – 1
116)
A)
Domain: (–, ); Range: [–1, )
B)
Domain: (–, ); Range: [0, )
61
C)
Domain: (–, ); Range: [1, )
D)
Domain: (–, ); Range: [0, )
Provide an appropriate response.
117)
The range of the square root function, given by f(x) =x, is .
117)
A)
( , )
B)
[0, )
C)
[0, )
D)
( , 0]
Find the equation of a circle satisfying the given conditions.
118)
Center: (0, –8); radius: 15
118)
A)
(x – 8)2+ y2=225
B)
x2+ (y – 8)2=15
C)
(x + 8)2+ y2=225
D)
x2+ (y + 8)2=15
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?
119)
x2+(y + 5)2
25 = 1
119)
A)
y1= 5 + 5 1 +x2, y2= 5 – 5 1 +x2
B)
y1= – 5 + 5 1 +x2, y2= – 5 – 5 1 +x2
C)
y1= – 5 + 5 1 –x2, y2= – 5 – 5 1 –x2
D)
y1= 5 + 5 1 –x2, y2= 5 – 5 1 –x2
Solve the problem. Round your answer to the nearest tenth.
120)
The roof of a building is in the shape of the top half of the hyperbola y2– 8x2=40, where x and y
are in meters. Refer to the figure and determine the height, h, of the outside walls.
a =8.0 m b =8.0 m
120)
A)
552.0 m
B)
8.5 m
C)
23.5 m
D)
72.0 m
Solve the problem by using a nonlinear system.
121)
The sum of the squares of the digits of a positive two–digit number is 85, and the tens digit is 1 less
than the units digit. Find the number.
121)
A)
56
B)
65
C)
76
D)
67
122)
A rectangular plot has area 126 yd2 with a perimeter of 46 yd. What is the length of one of the
longer sides?
122)
A)
13 yd
B)
14 yd
C)
16 yd
D)
12 yd
Graph the inequality.
123)
y x2+ 2x + 4
123)
A)
B)
64
C)
D)
Graph the rational function.
124)
f(x) =1
x – 3
124)
A)
B)
65
C)
D)
Graph the step function.
125)
f(x) =x – 5
125)
A)
B)
66
C)
D)
Find the center and radius of the circle whose equation is given. Graph the circle.
126)
(x – 1)2+(y – 1)2=16
126)
A)
center: (– 1, – 1); radius: 16
B)
center: (1, 1); radius: 16
67
C)
center: (1, 1); radius: 4
D)
center: (– 1, – 1); radius: 4
D)
Decide whether the statement is true or false.
127)
The x–intercepts of the ellipse with equation x2
49 +y2
16 = 1 are (7, 0) and (–7, 0).
127)
A)
True
B)
False
The hyperbola shown in the calculator–generated graph was graphed in 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?
128)
y2
49 –x2
9= 1
10
–15 15
–10
128)
A)
y1= 7 x2
9– 1, y2= – 7x2
9– 1
B)
y1= 3 x2+ 7, y2= – 3 x2+ 7
C)
y1= 7 x2– 9, y2= – 7 x2– 9
D)
y1= 7 x2
9+ 1, y2= – 7x2
9+ 1
Graph the function defined by a radical expression.
129)
f(x) =2x + 1
2
129)
69
A)
B)
C)
D)
Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle.
130)
y2=50 – x2
130)
A)
circle
B)
ellipse
C)
parabola
D)
hyperbola
Graph the system of inequalities.
70
131)
x2
9–y2
16
1
x2+ y2
36
131)
A)
B)
C)
D)
Graph the inequality.
71
132)
y –x2– 6x – 3
132)
A)
B)
C)
D)
Find the equation of a circle satisfying the given conditions.
133)
Center: (–9, 0); radius: 11
133)
A)
x2+ (y + 9)2=11
B)
(x – 9)2+ y2=121
C)
(x + 9)2+ y2=121
D)
x2+ (y – 9)2=11
Provide an appropriate response.
134)
True or false? The y–intercepts of the hyperbola with equation x2
81 –y2
49 = 1 are (9, 0) and (–9, 0).
134)
A)
False
B)
True
Find the equation of a circle satisfying the given conditions.
135)
Center: (5, –5); radius: 2
135)
A)
(x – 5)2+ (y + 5)2=2
B)
(x + 5)2+ (y – 5)2=4
C)
(x + 5)2+ (y – 5)2=2
D)
(x – 5)2+ (y + 5)2=4
Graph the rational function.
136)
f(x) =1
x+ 3
136)
73
A)
B)
C)
D)
Graph the circle.
137)
x2+ (y – 1)2=16
137)
74
A)
B)
C)
D)
Provide an appropriate response.
138)
The range of f(x) =x, the greatest integer function, is .
138)
A)
[0, )
B)
{. . . , –4, –2, 0, 2, 4, . . .}
C)
{. . . , –2, –1, 0, 1, 2, . . .}
D)
( , )
A