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Math Test 3 Questions with Answers
1.Write the domain in interval notation.
f(x)=x^2-9/x+3: (- , -3) u (-3, )
2.Refer to the graph of the function and complete the stateme as x -----> - , f(x)
as x -----> , f(:x-)7; -
3.Refer to the graph of the function and complete the stateme The domain is,
the range is,: (- , 5) u (5, ); (2, )
4.Determine the vertical asymptote(s) of the graph of the function. f(x)= x-2/ 8x^2 -
75x+27: x=9 and x= 3/
5.Determine the vertical asymptote(s) of the graph of the function. f(x)= x/ x^2+16:
none
6.a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. f(x)= x^2+8x^2-8/ 3x-7: a. No Horizontal asymptote b. not applicable
7.a. Identify the horizontal asymptote (if any).
2 / b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. s(x) = 2x - 10/ x^2+7x-4: a. y= b. (5,0)
8.a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal asymptote, determine the point where the graph crosses the horizontal asymptote. f(x) = 7x^2 - 6x + 3/ x^2+4: a. y= b. (-25/6, 7)
9.Identify the asymptotes.
f (x) = 4x^3 - 5x + 8/ 2x^2-3x+9: slant asymptote: y= 2x+
10.Identify the asymptotes.
f(x)= -3x^2+5/x: Vertical symptote: x=0; Slant asymptote: y= -3x
13.The graph of y = f (x) is given. Solve the inequality. f( x) e 0 : (- ,-
11. Graph the
function. f(x)= 3x/
x^2-2x-3:
12. Graph the
function. f(x)=-
x^2+4x-4/x:
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23.Evaluate the function for the given value of x. f(x) = x^2 + 2x,
g(x) = 5x - 1, (Go f)(2)= ?: (g • f)(2)= 39
24.Evaluate the function for the given value of x. g(x) = 3x - 8,
h(x) = 2 x-5, (hog)(2)=: ?undefined
25.Find the indicated function and write its domain in interval notation. r(x) = |-3x + 4|, n(x) = x -
9, (r n)(x) =: ?( r • n)(x)= |-3x + 31|; domain: (- , )
26.Find two functions f and g such that h(x) = (f g)(x).
h(x) = 4 11x - : 9 f(x)= 4 x and g(x)= 11x-
27.Find the indicated function and write its domain in interval notation. n(x) = x + 3, q(x) = 1 ,
(q n)(x) =: ?( q º n)(x)= 1/x-1; domain: (- ,1) u (1, )
28.Find two functions f and g such that h(x) = (f g)(x).
h(x)= 4/x+4: f(x)=4/x and g(x)= x+
29.A relation in x and y is given. Determine if the relation defines y as a one-to-one function
of x. x y 3.0 ,7. -8.4 ,-8. 2.4, - 9. -1.5, 7.45: No
30.Determine if the relation defines y as a one-to-one function of x.: No
31.Determine whether the two functions are inverses. f (x) = 4x - 2 and
g(x)= -2+x/4: No
32.Determine whether the two functions are inverses. f(x)=2/x-8 and
5 / g(x)= 2+8x/x: Yes
33.A one-to-one function is given. Write an expression for the inverse func- tion.
f(x)=3 x:- 8 f^- 1 (x)= x^3 + 8
34.A one-to-one function is given. Write an expression for the inverse func- tion.
f(x)= x+5/x-1: f^-1 (x) = 5+1x/x- 1
35.Evaluate the function at the given value of x. Round to 4 decimal places if necessary.
f (x) = 6^x; f (2.3): 61.
36.Evaluate the function at the given value of x. Round to 4 decimal places if necessary.
f(x)= (1/3)^x; f(-5): 243
37.Solve the problem.
The atmospheric pressure on an object decreases as altitude increases. If a is the height 37) (in km) above sea level, then the pressure P(a) (in mmHg) is approximated by P(a) = 760^e-0.13a. Determine the atmospheric pressure at 8.296 km. Round to the nearest whole unit: 258 mmHg
38.Solve the problem.
The population of bacteria culture was 2000 at noon, and was increasing at a rate of 10% 38) per hour. The number can be found using the function P(t) = 2,000(1.1)^t where t is the number of hours past noon. Predict the population 6 hours later, at 6 PM to the nearest whole number.: 3543
39.Solve the problem.
from 1995-2005, the hourly pay for lifeguards at an outdoor swimming pool increased by 5% per year. The hourly pay, P(t), in dollars, t yr after 1995 is given by P(t) = 6.00(1.05)^t. What was the hourly pay for
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49.Use the quotient property of logarithms to write the logarithm as a differ- ence of logarithms.
Then simplify if possible. ln(e/18): 1-ln(18)
50.Apply the power property of logarithms. log(3t - 7)4:
4 log (3t-7)
51.Apply the power property of logarithms. ln 5 x ^:
9 9/5ln x
52.Write the logarithm as a sum or difference of logarithms. Simplify each term as much as
possible. log8^x^4y^7: 4log8 x+ 7log8 y
53.Write the logarithm as a sum or difference of logarithms. Simplify each term as much as
possible. log6 5 x:/ 6 1/5log6 x - 1/
54.Write as the sum or difference of logarithms and fully simplify, if possible. Assume the variable
represents a positive real number. ln(8 ab/c^ 3 :d 1 ) /8 ln a +1/8 ln b-3 ln c-ln d
55.Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much
as possible. 3log2 m - 4log2 n: log2 m^3/n^
56.Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much
as possible. log10 50 + log10 2: 2
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57.Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much
as possible. 1/2 [10 ln (x - 8) + ln x - 2ln x]: ln[(x-8)^5/ x]
58.Solve the equation.
32^x+4 = 2^6x: {20}
59.Solve the equation. 7^(4x-
4)= (1/49)^(x-7): 3
60.solve the equation. write the solution set with the exact values given in terms of natural or
common logarithms. Also give approximate solutions to 4 decimal places, if necessary. 9^2x + 4 = 4^4x + 3: {3 ln 4 - 4 ln 9/2 ln 9 - 4 ln 4}; x= 4.
61.Solve the equation. Write the solution set with the exact solutions. Also give approximate
solutions to 4 decimal places if necessary. 24 log4(3p - 77) = 48: {31}
62.Solve the logarithmic equation.
-14 = -16 - log2(4x + 4): {-15/16}
63.Solve the logarithmic equation. log x = 1 -
log(x + 3): {2}
64.Solve the equation.
log7 (3p + 23) + log7 p = log7 36: {4/3}
65.Solve the problem.
If $25,000 is invested in an account earning 4.3% interest compounded con- tinuously, 65) determine how long it will take the money to triple. Round to the nearest year. Use the model A = Pert where A represents the future value of P dollars invested at an interest
