Question 1

Graph using a table of values and integer inputs between -3 and 3. Indicate whether the function is increasing or decreasing.
y =

Accepted Answer

decreasing   (Gridlines are spaced one unit apart.)

Question 2

Graph by the following function by translating the basic function y = bx, sketching the asymptote, and strategically plotting a few points to round out the graph. y = 2x - 1

Accepted Answer

A) 
 
(Gridlines are spaced one unit apart.) 
B) 
 
(Gridlines are spaced one unit apart.) 
C) 
 
(Gridlines are spaced one unit apart.) 
D) 
 
(Gridlines are spaced one unit apart.) 
A) 
 
(Gridlines are spaced one unit apart.) 
B) 
 
(Gridlines are spaced one unit apart.) 
C) 
 
(Gridlines are spaced one unit apart.) 
D) 
 
(Gridlines are spaced one unit apart.) B

Question 3

Write the equation in the simplified form bx = k (exponential term = constant). Do not solve.
1 - 4e0.2x = -35

Accepted Answer

e^0.2^x = 9

Question 4

Graph the logarithmic function.
f(x) = -ln(x + 1)

Accepted Answer

The answer of Graph the logarithmic function.
f(x) = -ln(x +...

Question 5

Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(-x - 2) = log(3x) - log x

Accepted Answer

A)  x = 0, -5 
B)  x = 0, 5 
C)  x = 5 
D)  No solution 
A)  x = 0, -5 
B)  x = 0, 5 
C)  x = 5 
D)  No solution

Question 6

Determine a likely candidate for the inverse function by reasoning and test points.
f(x) = x + 3

Accepted Answer

The answer of Determine a likely candidate for the inverse...

Question 7

Evaluate the expression using the change-of-base formula and either base 10 or base e. Answer in approximate form using 8 decimal places. log 3 27

Accepted Answer

A)  2.84767879 
B)  2.98768768 
C)  3.00000000 
D)  3.32345613 
A)  2.84767879 
B)  2.98768768 
C)  3.00000000 
D)  3.32345613

Question 8

Compute   . f(x) = x3 + 8

Accepted Answer

A)    , x ≥ 0 
B)    
C)    , x ≥ 8 
D)    
A)    , x ≥ 0 
B)    
C)    , x ≥ 8 
D)

Question 9

Use the properties of logarithms to write the expression as a single term.
ln(x + 7) + ln(7x)

Accepted Answer

The answer of Use the properties of logarithms to write...

Question 10

Solve the exponential equation and check your answer by substituting into the original equation.
2x = 8

Accepted Answer

Question 11

Determine the domain of the function.

Accepted Answer

A)  x $\in$ (-4, 2) 
B)  x $\in$ [-4, 2) 
C)  x $\in$ (-?, -4) $\cup$  (2, ?) 
D)  x $\in$ (-?, -4] $\cup$  (2, ?) 
A)  x $\in$ (-4, 2) 
B)  x $\in$ [-4, 2) 
C)  x $\in$ (-?, -4) $\cup$  (2, ?) 
D)  x $\in$ (-?, -4] $\cup$  (2, ?)

Question 12

Solve the exponential equation.   = 343

Accepted Answer

The answer of Solve the exponential equation.   =...

Question 13

Write the equation in the simplified form log b x = k (logarithmic term = constant). Do not solve. ln(x - 3) - ln x = -ln(5x)

Accepted Answer

A)    
B)  ln(5x3 - 15x2) = 0 
C)    
D)  ln(5x - 15) = 0 
A)    
B)  ln(5x3 - 15x2) = 0 
C)    
D)  ln(5x - 15) = 0

Question 14

Write the equation in logarithmic form. 24 = 16

Accepted Answer

A)  16 = log 2 4 
B)  4 = log 2 16 
C)  2 = log 4 16 
D)  16 = log 4 2 
A)  16 = log 2 4 
B)  4 = log 2 16 
C)  2 = log 4 16 
D)  16 = log 4 2

Question 15

Determine whether the graph is that of a one-to-one function. If not, give an example of how the definition of one-to-oneness is violated.   (Gridlines are spaced one unit apart.)

Accepted Answer

not one-to-one, fail

Question 16

Compute   . f(x) = 2x - 6

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Use a calculator to evaluate ln 401, rounded to six decimal places.

Accepted Answer

A)  4.992827 
B)  5.993961 
C)  7.117417 
D)  8.184048 
A)  4.992827 
B)  5.993961 
C)  7.117417 
D)  8.184048

Question 18

Solve the exponential equation. 27x + 2  = 3

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

For accounts where interest is compounded annually, the amount A accumulated or due depends on the principal p, interest rate r, and the time t in years according to the formula A = p(1 + r)t. Find t when A = $994.93, p = $850, and r = 6.5%. Round your answer to the nearest tenth.

Accepted Answer

Question 20

Use the following to answer questions :
A lab technician wishes to grow a culture of 800,000 bacteria, which are known to double in 16 hours. The technician begins with 9000 bacteria.
-How many hours will it take for the culture to produce the 100,000 bacteria? Round your answer to the nearest hour.

Accepted Answer

A)  64 hours 
B)  66 hours 
C)  69 hours 
D)  72 hours 
A)  64 hours 
B)  66 hours 
C)  69 hours 
D)  72 hours

Graph using a table of values and integer inputs between -3 and 3. Indicate whether the function is increasing or decreasing. y =

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. y = 2^x ^{- 1}

Write the equation in the simplified form b^x = k (exponential term = constant). Do not solve. 1 - 4e^0.2^x = -35

Graph the logarithmic function. f(x) = -ln(x + 1)

Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(-x - 2) = log(3x) - log x

Determine a likely candidate for the inverse function by reasoning and test points. f(x) = x + 3

Evaluate the expression using the change-of-base formula and either base 10 or base e. Answer in approximate form using 8 decimal places. log₃27

Compute . f(x) = x³ + 8

Use the properties of logarithms to write the expression as a single term. ln(x + 7) + ln(7x)

Solve the exponential equation and check your answer by substituting into the original equation. 2^x = 8

Determine the domain of the function.

Solve the exponential equation. = 343

Write the equation in the simplified form log_bx = k (logarithmic term = constant). Do not solve. ln(x - 3) - ln x = -ln(5x)

Write the equation in logarithmic form. 2⁴ = 16

Determine whether the graph is that of a one-to-one function. If not, give an example of how the definition of one-to-oneness is violated. (Gridlines are spaced one unit apart.)

Compute . f(x) = 2x - 6

Use a calculator to evaluate ln 401, rounded to six decimal places.

Solve the exponential equation. 27^x^{+ 2} = 3

For accounts where interest is compounded annually, the amount A accumulated or due depends on the principal p, interest rate r, and the time t in years according to the formula A = p(1 + r)^t.Find t when A = $994.93, p = $850, and r = 6.5%. Round your answer to the nearest tenth.

Use the following to answer questions : A lab technician wishes to grow a culture of 800,000 bacteria, which are known to double in 16 hours. The technician begins with 9000 bacteria. -How many hours will it take for the culture to produce the 100,000 bacteria? Round your answer to the nearest hour.

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Exam 4: Exponential and Logarithmic Functions

Graph using a table of values and integer inputs between -3 and 3. Indicate whether the function is increasing or decreasing. y =

Graph by the following function by translating the basic function y = bx, sketching the asymptote, and strategically plotting a few points to round out the graph. y = 2x - 1

Write the equation in the simplified form bx = k (exponential term = constant). Do not solve. 1 - 4e0.2x = -35

Graph the logarithmic function. f(x) = -ln(x + 1)

Solve using any appropriate method. Clearly identify any extraneous roots. If there are no solutions, so state. log(-x - 2) = log(3x) - log x

Determine a likely candidate for the inverse function by reasoning and test points. f(x) = x + 3

Evaluate the expression using the change-of-base formula and either base 10 or base e. Answer in approximate form using 8 decimal places. log 3 27

Compute . f(x) = x3 + 8

Use the properties of logarithms to write the expression as a single term. ln(x + 7) + ln(7x)

Solve the exponential equation and check your answer by substituting into the original equation. 2x = 8

Determine the domain of the function.

Solve the exponential equation. = 343

Write the equation in the simplified form log b x = k (logarithmic term = constant). Do not solve. ln(x - 3) - ln x = -ln(5x)

Write the equation in logarithmic form. 24 = 16

Determine whether the graph is that of a one-to-one function. If not, give an example of how the definition of one-to-oneness is violated. (Gridlines are spaced one unit apart.)

Compute . f(x) = 2x - 6

Use a calculator to evaluate ln 401, rounded to six decimal places.

Solve the exponential equation. 27x + 2 = 3

For accounts where interest is compounded annually, the amount A accumulated or due depends on the principal p, interest rate r, and the time t in years according to the formula A = p(1 + r)t. Find t when A = $994.93, p = $850, and r = 6.5%. Round your answer to the nearest tenth.

Equations and Inequalities

Relations, Functions and Graphs

Polynomial and Rational Functions

Introduction to Trigonometric Functions

Trigonometric Identities, Inverses, and Equations

Applications of Trigonometry

Systems of Equations and Inequalities

Analytical Geometry

Additional Topics in Algebra

Bridges to Calculus - an Introduction to Limits

Review of Basic Concepts and Skills

Filters

Graph by the following function by translating the basic function y = b^x, sketching the asymptote, and strategically plotting a few points to round out the graph. y = 2^x ^{- 1}

Write the equation in the simplified form b^x = k (exponential term = constant). Do not solve. 1 - 4e^0.2^x = -35

Evaluate the expression using the change-of-base formula and either base 10 or base e. Answer in approximate form using 8 decimal places. log₃27

Compute . f(x) = x³ + 8

Solve the exponential equation and check your answer by substituting into the original equation. 2^x = 8

Write the equation in the simplified form log_bx = k (logarithmic term = constant). Do not solve. ln(x - 3) - ln x = -ln(5x)

Write the equation in logarithmic form. 2⁴ = 16

Solve the exponential equation. 27^x^{+ 2} = 3

For accounts where interest is compounded annually, the amount A accumulated or due depends on the principal p, interest rate r, and the time t in years according to the formula A = p(1 + r)^t.Find t when A = $994.93, p = $850, and r = 6.5%. Round your answer to the nearest tenth.