Name________________________________________ Date _________________________ Period ____________ Discrete Math Chapter 10 Test Review Give the domain of the function. 7) Find f(k) when f(x) = 3x 2 + 4x + 5. 1 1) f(x) = x2 + 3x - 10
2) f(x) =
Graph the rational function. 1 8) f(x) = x-4
20 - x
y 6 4
x+3 x-9
3) f(x) =
2
-6
-4
-2
2
4
6
x
-2 -4 -6
4) f(x) = 7x2 + 8x + 5
9) y =
x-2 x+3 5
Evaluate the function.
4
x-6 5) Find f(4) when f(x) = . x+9 A)
2 5
C) -
2 3
y
3
B) -
2 13
D) -
1 2
2 1 -10 -8 -6 -4 -2 -1 -2 -3 -4 -5
Solve the equation.
1 10) 2(5 - 3x) = 16
6) Find f(-3) when f(x) = 3x2 + 3x - 7.
1
2
4
6
8
10 x
Give the possible values for the degree of the polynomial and the sign (+ or -) of the x n term.
Write the exponential equation in logarithmic form. 1 16) 4-3 = 64
11) 6
y
17) 6 x
-6
-6
Write the logarithmic equation in exponential form. 1 18) log4 = -2 16
Write the logarithmic equation in exponential form. 15) log2 32 = 5
2
Solve the problem. Round answers to the nearest hundredth. 22) ey + 3 = 7
26) The number of acres in a landfill decreases according to the function B = 4600e-0.02t,
Solve the problem. 23) Find the present value of the deposit. $6000 at 10% compounded monthly for 10 years
27) In the formula N = Iekt , N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain country to triple if its annual growth rate is 3.4%? Round to the nearest year.
where t is measured in years. How many acres will the landfill have after 9 years?
24) Find the present value of the deposit. $500 at 4% compounded continuously for 10 years
28) The number of books in a small library increases according to the function B = 3500e 0.05t, where t is measured in years. How many books will the library have after 6 years?
25) A bacteria colony doubles in 7 hr. How long does it take the colony to triple? Use N = N0 2t/T, where N0 is the initial number of bacteria and T is the time in hours it takes the colony to double. (Round to the nearest hundredth, as necessary.)
29) In the formula A(t) = A0ekt , A(t) is the amount of radioactive material remaining from an initial amount A0 at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope decays at a rate of 0.25% annually. Determine the half-life of this isotope, to the nearest year.
3
30) In the formula A(t) = A0ekt, A(t) is the amount of radioactive material remaining from an initial amount A0 at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 60% of the carbon-14 it originally contained, what is the approximate age of the artifact? (carbon-14 decays at the rate of 0.0125% annually.) (Round to the nearest year.)
