End of Semester Test: Algebra 2B practice
(Plato, 11 wrong – marked)
Ms. Walker's class set up an online fund with a goal to raise $1,280 to go on a field trip. Ms.
Walker starts the fund by depositing $5. Each week the balance of the fund is twice the balance
of the previous week. Which equation can be used to find the number of weeks, x, after which
the balance of the fund will reach 1,280, and how many weeks will it take to reach the class
goal? - Answer: 5(2)^x = 1,280; x = 8
Sam purchased a new car for $17,930. The value of the car depreciated by 19% per year. -
Answer: WRONG - 17,930 (0.81)^x _< 1900
Which expressions are equivalent to the given expression. - Answer: log10(20x^5) - 1, log10
(10x)
Match each logarithmic equation to its corresponding x-value - Answer: log5x=4 —> 625
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, log4x=2 —> 16
log10x=3 —> 1,000
log2x=5 —> 32
What value of x satisfies this equation? 1.5(4)^2x = 12 - Answer: 0.75
What is the approximate solution to this equation? 4Inx - 8 = 12 - Answer: x ≈ 148.4
If function f is the parent exponential function f(x) = e^x. What is the equation of transformed
function g in terms - Answer: g(x) = 3f(x)
Consider the graph of the function f(x) = 10^x, what is the range of function g if g(x) = -2f(x) + 1 -
Answer: (- infinity, 1)
Which statements are true about the graph of function f? - Answer: PARTIALLY WRONG - The
graph has a range of {y| - infinity < x < infinity} and decreases as x approaches 0
(this is correct but it's not the only answer)
Consider the graph of the function f(x) = In x, match each transformation of function f with a
feature of the transformed function. - Answer: j(x) = f(x) -1/2 —> vertical asymptote of x = 0
h(x) = f(x - 1/2) —> y-intercept at (0,-1/2) WRONG (should be x-intercept at (1.5,0) by default
but idk)
g(x) = -1/2f(x - 2) —> function decreases as x increases
Determine the explicit for of the function that describes the sequence below, 16, 24, 36, 54... -
Answer: f(n) = 16(3/2)^(n - 1)
Natalie buys a new car. At the end of the first month, the odometer on the car reads 800 miles.
From past experience, she expects to drive 900 miles a month. Select all functions that can be
Page 2 of 7
(Plato, 11 wrong – marked)
Ms. Walker's class set up an online fund with a goal to raise $1,280 to go on a field trip. Ms.
Walker starts the fund by depositing $5. Each week the balance of the fund is twice the balance
of the previous week. Which equation can be used to find the number of weeks, x, after which
the balance of the fund will reach 1,280, and how many weeks will it take to reach the class
goal? - Answer: 5(2)^x = 1,280; x = 8
Sam purchased a new car for $17,930. The value of the car depreciated by 19% per year. -
Answer: WRONG - 17,930 (0.81)^x _< 1900
Which expressions are equivalent to the given expression. - Answer: log10(20x^5) - 1, log10
(10x)
Match each logarithmic equation to its corresponding x-value - Answer: log5x=4 —> 625
Page 1 of 7
, log4x=2 —> 16
log10x=3 —> 1,000
log2x=5 —> 32
What value of x satisfies this equation? 1.5(4)^2x = 12 - Answer: 0.75
What is the approximate solution to this equation? 4Inx - 8 = 12 - Answer: x ≈ 148.4
If function f is the parent exponential function f(x) = e^x. What is the equation of transformed
function g in terms - Answer: g(x) = 3f(x)
Consider the graph of the function f(x) = 10^x, what is the range of function g if g(x) = -2f(x) + 1 -
Answer: (- infinity, 1)
Which statements are true about the graph of function f? - Answer: PARTIALLY WRONG - The
graph has a range of {y| - infinity < x < infinity} and decreases as x approaches 0
(this is correct but it's not the only answer)
Consider the graph of the function f(x) = In x, match each transformation of function f with a
feature of the transformed function. - Answer: j(x) = f(x) -1/2 —> vertical asymptote of x = 0
h(x) = f(x - 1/2) —> y-intercept at (0,-1/2) WRONG (should be x-intercept at (1.5,0) by default
but idk)
g(x) = -1/2f(x - 2) —> function decreases as x increases
Determine the explicit for of the function that describes the sequence below, 16, 24, 36, 54... -
Answer: f(n) = 16(3/2)^(n - 1)
Natalie buys a new car. At the end of the first month, the odometer on the car reads 800 miles.
From past experience, she expects to drive 900 miles a month. Select all functions that can be
Page 2 of 7
