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Math 114-Quiz 1 - Quiz 1
Mathematics for Liberal Arts (Liberty
University)
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Math 114-Quiz 1
1.) Let f(x)=SQR(x-4) and
g(x)=4+x^2 Verify that f
and g are inverses
f(g(x))=x and g(f(x))=x
2.) Graph f, g, and y=x in the same coordinate system and identify each graph-
on the quiz
3.) 00:05
01:15
4.) Domain f is
(4,0)
5.) Range g is
(0,oo)
6.) Rang of f
(0, 2)
7.) Domain g is
(-oo, oo)
8.) Function?
{(-6, -4), (-3, -6), (2, -4), (2, -8)}
No
9.) Function?
{(-1, 7), (2, -2), (6, 7), (9, 9), (10, -4)}
yes
6.) Given that f(x)=x/11-x, find f(-2/5)
-2/57
7.) Given that h(x)=4x - sqrx^2-3, find
h(-x)
-4x - sqrx^2-3
8.) visually estimate its domain and
range t(x)=sqr3-x
Domain = (-oo, 3]; range= [0, oo)
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9.) h(x)= lxl - 4
Domain = (-oo, oo); range= [-4, oo)
10.) Solve
The function H described by H(x)=2.75x + 71.48 can be used to
estimate the height, in centimeters, of a woman whose humerus (the
bone from the elbow to the shoulder) is x cm long. Estimate the
height of a woman whose humerus is
35.5 cm long.
169.105 cm
11.) Solve
The cost of manufacturing a molded part is related to the quantity
produced during a production run. When 100 parts are produced, the
cost is $300. When 600 parts are produced, the cost is $4300. What is
the average cost per part?
$8.00 per cent
12.) To convert a temperature from degrees Celsius to degrees Fahrenheit,
you multiply the temperature in degrees Celsius by 1.8 and then add 32 to
the result. Express F as a linear function of c.
F(c)=1.8+32
13.) Write a slope-intercept
m=-3/2, passes through (-
2, -2) y=-3/2x-5
14.) Parallel, perpendicular, or
neither 3x-6y=14
18x+9y14
perpendicular
15.) Put the answer in the slope
Through (3, -6), perpendicular to -3x-
7y=33 y=7/3x-13
16.) Simplify. Write in a+bi
4+sqr7i/3-9i
12-9sqr7/90 + 36+3sqr7/90i
17.)
Si
mp
lify
i^1
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9
-i
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18.) Solve
49x^2+28x-32=0
-8/49, -24/49
19.) 10x^2=60x
6
20.) Solve by completing the
square x^2-12x+52=0
6 +/- 4i
21.) Use a graphing calculator to find zeros. Round to three decimal places.
3x^2+16x+14=0
-4.23, -1.103
22.) Solve
How long would it take an object to fall freely from the top of a tower
1785 ft tall? (Use the formula s=16t^2)
About 10.6 sec
23.) Solve
1/A=1/m+1/t,
for t mA/m-A
24.) sqr3x+1=3+sqrx-4
5,8
25.) Given that P(x)= 12x^4 - 7x^3+ 98^2- 63x- 90; and P(-3i)=0, find the
remaining roots.
3i, -3i, 145, -131
26.) Analyze the function algebraically. List its vertical asymptote(s),
horizontal asymptote, x-intercept, y-intercept, and check if the graph
crosses its horizontal asymptote. Sketch a complete graph of the
function.
f(x)=x+3/x^2+3x-10
vertical asymptotes:
-5,2
horizontal
asymptotes: -3 x-
intercept:none
y-intercept: -
3/10 Graph on
quiz
27.) Analyze the function algebraically. List vertical asymptotes, horizontal
asymptote,
x-intercept, y-intercept, and check if the graph crosses its horizontal
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asymptote. Sketch a complete graph of the function.
f(x)=2x+6/x-3
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28.) Vertical asymptote: 3
horizontal: -3,2
x-intercept: 3
y-intercept:
-2 Graph on
quiz
29.) Combine
2Inx + 5Iny -
logz
Inx^2y^5/z
30.) Combine
log 3^sqrx^5y^7/z^3
1/3[5logx + 7logy -
3logz]
31.) Combine
logx^2/sqry
2logx-
1/2logy
32.) 3^x=4
x~1.2
61
33.) log2(x^2-2x)=log2(3x-6)
S.S. ={3}
34.) 3=1.06^x
x~19 years
35.) logx-log5=log2-log(x-3)
S.S. = {5}
36.) x^logx=100x
x=100, 0.1
37.) COMPOUND INTEREST
How many years, to the nearest year, will it take a sum of the money
to double if it is invested at 15% compounded annually?
t~5 years
