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Questions and Answers
The function f(x) = x - 3/x² + 2x - 8 is undefined when x equals
The function f(x) = x - 3/x² + 2x - 8 is undefined when x equals
2 or -4
Which expression is equivalent to (3k - 2i)², where i is the imaginary unit?
Which expression is equivalent to (3k - 2i)², where i is the imaginary unit?
The roots of the equation x² + 2x + 5 = 0 are
The roots of the equation x² + 2x + 5 = 0 are
-1 + 2i and -1 - 2i
The solution set for the equation √x + 14 - √2x + 5 = 1 is
The solution set for the equation √x + 14 - √2x + 5 = 1 is
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As x increases from 0 to π/2, the graph of the equation y = 2 tan x will
As x increases from 0 to π/2, the graph of the equation y = 2 tan x will
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Which equation represents a parabola with the focus at (0, -1) and the directrix y = 1?
Which equation represents a parabola with the focus at (0, -1) and the directrix y = 1?
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Which diagram represents an angle, α, measuring 13π/20 radians drawn in standard position, and its reference angle, θ?
Which diagram represents an angle, α, measuring 13π/20 radians drawn in standard position, and its reference angle, θ?
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What are the zeros of P(m) = (m² - 4)(m² + 1)?
What are the zeros of P(m) = (m² - 4)(m² + 1)?
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What is the average decreasing rate of change per year of the value of the car from June 2012 to June 2014?
What is the average decreasing rate of change per year of the value of the car from June 2012 to June 2014?
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What equation approximates the amount of Iridium-192 present after t days?
What equation approximates the amount of Iridium-192 present after t days?
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What proportion of the ball bearings will have a diameter less than 3.7 cm if the distribution is normal with a mean of 4 cm and a standard deviation of 0.2 cm?
What proportion of the ball bearings will have a diameter less than 3.7 cm if the distribution is normal with a mean of 4 cm and a standard deviation of 0.2 cm?
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Which statements regarding the polynomial equation of degree three, p(x), with x-intercepts at -2, 10, and 14 could be true? (Select all that apply)
Which statements regarding the polynomial equation of degree three, p(x), with x-intercepts at -2, 10, and 14 could be true? (Select all that apply)
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Which expression is equivalent to (4x³ + 9x - 5)/(2x - 1), where x ≠ 1/2?
Which expression is equivalent to (4x³ + 9x - 5)/(2x - 1), where x ≠ 1/2?
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The inverse of the function f(x) = (x + 1)/(x - 2) is
The inverse of the function f(x) = (x + 1)/(x - 2) is
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Which expression has been rewritten correctly to form a true statement?
Which expression has been rewritten correctly to form a true statement?
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At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to
At a 95% confidence level, the proportion of New York City residents with hypertension and the margin of error are closest to
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Which scenario is best described as an observational study?
Which scenario is best described as an observational study?
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Which sinusoid has the greatest amplitude?
Which sinusoid has the greatest amplitude?
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Study Notes
Function Undefined Points
- The function f(x) = (x - 3) / (x² + 2x - 8) is undefined at x = 2 and x = -4.
Equivalent Expressions
- The expression equivalent to (3k - 2i)² is 9k² - 12ki - 4.
Roots of Quadratic Equation
- The roots of x² + 2x + 5 = 0 are -1 + 2i and -1 - 2i.
Solution Set
- The solution set for √x + 14 - √(2x + 5) = 1 is {2}.
Graph Behavior
- As x increases from 0 to π/2, the graph of y = 2 tan x increases without limit.
Parabola Equation
- The equation representing a parabola with a focus at (0, -1) and directrix y = 1 is x² = -4y.
Angle Measurement
- An angle measuring 13π/20 radians in standard position has a reference angle θ positioned near the x-axis.
Zeros of Polynomial
- The zeros of P(m) = (m² - 4)(m² + 1) are 2, -2, i, and -i.
Car Depreciation Rate
- The average decreasing rate of change in the car's value from June 2012 to June 2014 is approximately $2450 per year.
Half-Life of Isotope
- After t days, the amount of Iridium-192 present, starting from 100 grams, is approximated by A = 100(0.990656)^t.
Normal Distribution Proportion
- In a normal distribution of ball bearings, with a mean of 4 cm and standard deviation of 0.2 cm, approximately 6.68% will have a diameter less than 3.7 cm.
Polynomial Volume Model
- For the polynomial p(x) with x-intercepts at -2, 10, and 14, true statements include:
- A.) The equation is p(x) = (x + 2)(x - 10)(x - 14).
- D.) The maximum volume of the box is approximately 56.
Correct Expression Rewrite
- The correct rewriting of the expression is (x+2)² + 2(x+2) - 8 = (x + 6)x.
Proportion from Observational Study
- In a 2004 study in NYC, 212 out of 1334 participants had hypertension, yielding a proportion of approximately 0.16 with a margin of error of approximately 0.02 at a 95% confidence level.
Observational Study Scenario
- An observational study occurs when a researcher gathers data on a potential link between attendance and grades.
Sinusoid Amplitude
- The sinusoid with the greatest amplitude is described by the equation y = -5sin(θ - 1) - 3.
Studying That Suits You
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Description
Test your knowledge with our flashcards based on the August 2017 Algebra 2 Regents exam. Each card presents a question or equation followed by its answer, covering key concepts in algebra and functions. Perfect for revision and practice ahead of your exams!
