AnswersVOA Math VT Advanced Algebra and Functions CR 1ADiagnostic PreTest

Diagnostic PreTest Answers

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What is the value of x if

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What are the domain and range of ?

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The domain is all real numbers. The range is all real numbers.
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The domain is all real numbers. The range is all real numbers greater than zero.
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The domain is all real numbers greater than zero. The range is all real numbers.
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The domain is all real numbers greater than zero. The range is all real numbers greater than zero.
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What is the solution to the equation below?

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What are the domain and range of ?

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domain: x > –6; range: y > 4
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domain: x > –6; range: all real numbers
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domain: x > 6; range: y > –4
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domain: x > 6; range: all real numbers
5

The general equation for depreciation is given by y = A(1 – r)t, where y = current value, A = original cost, r = rate of depreciation, and t = time, in years. A car was purchased 6 years ago for $25,000. If the annual depreciation rate is 11%, which equation can be used to determine the approximate current value of the car?

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Which function is graphed below?

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y = one-third (3) Superscript x
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y = 3 (one-third) Superscript x
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y = (one-half) Superscript x Baseline + 2
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y = (2) Superscript x Baseline minus 1
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Which function is shown in the graph below?

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y = log Subscript one-sixth Baseline x
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y = log Subscript 0.5 Baseline x
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y = log Subscript 1 Baseline x
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y = log Subscript 6 Baseline x
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Isabel deposits $6,000 into an account that earns 1.5% interest compounded monthly. Assuming no more deposits and no withdrawals are made, how much money is in the account after 4 years?Compound interest formula:t = years since initial depositn = number of times compounded per yearr = annual interest rate (as a decimal)P = initial (principal) investmentV(t) = value of investment after t years

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$6,360.00
B
$6,370.78
C
$7,180.89
D
$10,892.13
9

The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.

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2 years
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9 years
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17 years
D
22 years
10

Which graph represents an exponential growth function?

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On a coordinate plane, a line rapidly decreases and then levels off.
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On a coordinate plane, a line increases gradually.
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On a coordinate plane, a line decreases gradually.
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On a coordinate plane, a line is level and then curves upwards rapidly.
Option D
11

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. Which equation models the concentration of hydrogen ions (H+) of a solution whose pH is 7.2?

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[H+] = log7.2
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[H+] = -log7.2
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[H+] =
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[H+] =
Option D
12

What is the solution set of the quadratic inequality 4(x + 2)2 0?

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Which graph most likely shows a system of equations with one solution?

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The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle?

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Which represents the solution(s) of the graphed system of equations, y = x2 + x – 2 and y = 2x – 2?

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(–2, 0) and (0, 1)
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(0, –2) and (1, 0)
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(–2, 0) and (1, 0)
D
(0, –2) and (0, 1)
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What are the solution(s) of ?

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or
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x = 2
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x = 4
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What are the solutions of ?

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or
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18

Solve for in the equation .

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x = five-halves plus-or-minus StartFraction StartRoot 29 EndRoot Over 2 EndFraction
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x = five-halves plus-or-minus StartFraction StartRoot 41 EndRoot Over 4 EndFraction
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x = five-fourths plus-or-minus StartFraction StartRoot 29 EndRoot Over 2 EndFraction
Option C
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x = five-fourths plus-or-minus StartFraction StartRoot 41 EndRoot Over 4 EndFraction
Option D
19

Jerald jumped from a bungee tower. If the equation that models his height, in feet, is h = –16t2 + 729, where t is the time in seconds, for which interval of time is he less than 104 feet above the ground?

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t > 6.25
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–6.25 < t < 6.25
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t < 6.25
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20

The first step in determining the solution to the system of equations, y = –x2 – 4x – 3 and y = 2x + 5, algebraically is to set the two equations equal as –x2 – 4x – 3 = 2x + 5. What is the next step?

A
Set y = 0 in y = –x2 – 4x – 3.
B
Factor each side of the equation.
C
Use substitution to create a one-variable equation.
D
Combine like terms onto one side of the equation.

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