Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
187)
3x2– 4x 7
187)
A)
–1, 7
3
B)
–1, 7
3
C)
(–, –1) 7
3,
D)
(–, –1] 7
3,
Solve the problem.
188)
The revenue achieved by selling x graphing calculators is figured to be x(50 – 0.5x) dollars. The cost
of each calculator is $22. How many graphing calculators must be sold to make a profit (revenue –
cost) of at least $379.50?
188)
A)
between 30 and 40 calculators
B)
between 25 and 31 calculators
C)
between 24 and 32 calculators
D)
between 23 and 33 calculators
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
189)
(x +7)(x –5)
x – 1 0
189)
A)
[–7, 1) [5, )
B)
(–, –7]
(1, 5]
C)
[–7, 1] [5, )
D)
(–, –7]
[5, )
Solve.
190)
If the voltage, V, in an electric circuit is held constant, the current, I, is inversely proportional to the
resistance, R. If the current is 420 milliamperes when the resistance is 2 ohms, find the current
when the resistance is 14 ohms.
190)
A)
2940 milliamperes
B)
60 milliamperes
C)
120 milliamperes
D)
2933 milliamperes
Find the x–intercepts of the polynomial function. State whether the graph crosses the x–axis, or touches the x–axis and
turns around, at each intercept.
191)
f(x) =x3+ 11x2+ 40x + 48
191)
A)
–4, touches the x–axis and turns around;
–3, crosses the x–axis.
B)
4, crosses the x–axis;
–4, touches the x–axis and turns around;
–3, crosses the x–axis.
C)
–4, crosses the x–axis;
–3, touches the x–axis and turns around
D)
4, crosses the x–axis;
–4, crosses the x–axis;
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.
192)
3x3–x2–21x +7= 0
192)
A)
{3, 7, –7}
B)
{–1
3, 7, –7}
C)
{1
3, 7, –7}
D)
{–3, 7, –7}
Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of
the minimum or maximum point.
193)
f(x) =2x2– 2x – 3
193)
A)
minimum; 1
2, –7
2
B)
minimum; –7
2, 1
2
C)
maximum; 1
2, –7
2
D)
maximum; –7
2, 1
2
Write an equation that expresses the relationship. Use k for the constant of proportionality.
194)
p varies directly as q and inversely as r.
194)
A)
p+q–r= k
B)
p=kq
r
C)
p=kr
q
D)
pqr = k
–3, crosses the x–axis.
Determine whether the graph shown is the graph of a polynomial function.
195)
195)
A)
not a polynomial function
B)
polynomial function
Find the coordinates of the vertex for the parabola defined by the given quadratic function.
196)
f(x) = – x2+ 8x – 4
196)
A)
(8, –4)
B)
(–4, –20)
C)
(–4, –52)
D)
(4, 12)
Divide using synthetic division.
197)
(x2+ 14x + 45) ÷ (x + 5)
197)
A)
x2+ 9
B)
x + 9
C)
x3– 40
D)
x – 40
Write an equation that expresses the relationship. Use k as the constant of variation.
198)
w varies jointly as x and the cube of y.
198)
A)
wxy3= k
B)
w= k +x+y3
C)
w+x+y3= k
D)
w= kxy3
Find the x–intercepts (if any) for the graph of the quadratic function.
199)
5x2+ 12x + 3 = 0
Give your answers in exact form.
199)
A)
–6±51
5, 0
B)
–6±21
5, 0
C)
–6±21
10 , 0
D)
–12 ±21
5, 0
Solve the problem.
200)
A person standing close to the edge on top of a 128–foot building throws a baseball vertically
upward. The quadratic function s(t) = – 16t2+ 64t +128 models the ball’s height above the ground,
s(t), in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum
height? Round to the nearest tenth of a second if necessary.
200)
A)
1.5 seconds
B)
5.5 seconds
C)
2 seconds
D)
192 seconds
Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots.
201)
x3– 3x2– x + 3 = 0
201)
A)
{1, –1, –3}
B)
{1, 1, 3}
C)
{1, –1, 3}
D)
{–1, 1, –3}
Divide using long division.
202)
–4t4+ 18t3+ 8t2– 60t – 40
2t2– 4t – 4
202)
A)
–2t2+ 5t – 10
B)
–2t2+ 5t + 10
C)
–2t2+ 6t + 10
D)
–2t2– 5t + 10
Determine the maximum possible number of turning points for the graph of the function.
203)
f(x) =x4( x4+ 2)(6x + 4)
203)
A)
9
B)
48
C)
4
D)
8
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or –1 and make
the degree of the function as small as possible.
204)
Crosses the x–axis at –1, 0, and 3; lies above the x–axis between –1 and 0; lies below the x–axis
between 0 and 3.
204)
A)
f(x) =x3– 2x2– 3x
B)
f(x) =x3+ 2x2– 3x
C)
f(x) = – x3– 2x2+ 3x
D)
f(x) = – x3+ 2x2+ 3x
A
Determine the constant of variation for the stated condition.
205)
t varies jointly as r and s, and t=1872 when r=36 and s=13.
205)
A)
k =1
4
B)
k =9
C)
k =1
9
D)
k =4
D
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
206)
f(x) =x5–6x2+4x +21
206)
A)
± 1, ±1
7, ±1
3, ±1
21 , ±7, ±3, ±21
B)
± 1, ±7, ±3
C)
± 1, ±7, ±3, ±21
D)
± 1, ±1
7, ±1
3, ±1
21
C
80
D
Write the equation of a polynomial function with the given characteristics. Use a leading coefficient of 1 or –1 and make
the degree of the function as small as possible.
207)
Touches the x–axis at 0 and crosses the x–axis at 4; lies above the x–axis between 0 and 4.
207)
A)
f(x) = – x3+4x2
B)
f(x) =x3–4x2
C)
f(x) = – x3–4x2
D)
f(x) =x3+4x2
Find the y–intercept for the graph of the quadratic function.
208)
f(x) =(x + 1)2–1
208)
A)
(0, –1)
B)
(0, 2)
C)
(0, 1)
D)
(0, 0)
Solve the problem.
209)
The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room
and the height of the wall. If a room with a perimeter of 75 feet and 8–foot walls requires 6 quarts
of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 45 feet
and 6–foot walls.
209)
A)
270 quarts
B)
27 quarts
C)
5.4 quarts
D)
2.7 quarts
Answer Key
Testname: C3
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Answer Key
Testname: C3
Answer Key
Testname: C3
Answer Key
Testname: C3
Answer Key
Testname: C3
Answer Key
Testname: C3