Algebra 2 Regents Flashcards
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Questions and Answers

How do you find linear regression?

Go to stat, list, calc, and ensure stat diagnostics is on.

What defines a function?

A relationship from one set (domain) to another set (range) with each element of the domain assigned to exactly one element of the range.

What is a one-to-one function?

A function where each element of the range is paired with exactly one element of the domain.

Mutually exclusive events can occur at the same time.

<p>False (B)</p> Signup and view all the answers

What is an extraneous root?

<p>A solution that does not work in the original problem.</p> Signup and view all the answers

What is the horizontal line test used for?

<p>To determine if a function is one-to-one.</p> Signup and view all the answers

What does the vertical line test determine?

<p>If a curve is the graph of a function.</p> Signup and view all the answers

Provide an example of set notation.

<p>{x | x &gt; 0}</p> Signup and view all the answers

What is interval notation for '5 greater than or equal to x'?

<p>[5, ∞)</p> Signup and view all the answers

How do you complete the square?

<p>(B/2)^2 = C</p> Signup and view all the answers

What is the axis of symmetry formula?

<p>-b/2a</p> Signup and view all the answers

State the quadratic formula.

<p>x = (-b ± √(b² - 4ac)) / 2a</p> Signup and view all the answers

What is the vertex form of a quadratic equation?

<p>y = a(x - h)² + k</p> Signup and view all the answers

What represents a horizontal shift in a function?

<p>f(x - h)</p> Signup and view all the answers

What represents a vertical shift in a function?

<p>f(x) + k</p> Signup and view all the answers

How do you reflect a function over the x-axis?

<p>(x, y) --&gt; (x, -y)</p> Signup and view all the answers

How do you reflect a function over the y-axis?

<p>(-x, y)</p> Signup and view all the answers

What is vertical dilation?

<p>a * f(x) where a &gt; 1 indicates vertical stretch.</p> Signup and view all the answers

How does horizontal dilation affect a function?

<p>(1/b)(x), y with b &gt; 1.</p> Signup and view all the answers

An even function satisfies f(-x) = f(x).

<p>True (A)</p> Signup and view all the answers

An odd function satisfies f(-x) = -f(x).

<p>True (A)</p> Signup and view all the answers

What are conjugates?

<p>(a + bi) and (a - bi)</p> Signup and view all the answers

What is the additive inverse?

<p>A + bi to -a - bi</p> Signup and view all the answers

What is the multiplicative inverse?

<p>1/(a + bi), can't keep i in the denominator.</p> Signup and view all the answers

How do you find the quadratic equation's a, b, and c with roots?

<p>(R1 + R2) = -B/a; (R1 * R2) = c/a.</p> Signup and view all the answers

What is the vertical asymptote equation?

<p>B(x) = 0</p> Signup and view all the answers

What is the horizontal asymptote equation?

<p>Y = a(x)/b(x)</p> Signup and view all the answers

What is the asymptote parent function?

<p>Y = 1/x</p> Signup and view all the answers

How many horizontal asymptotes are there?

<p>More than one.</p> Signup and view all the answers

How do you transform an asymptote?

<p>(A/(x-h)) + k</p> Signup and view all the answers

What is the formula for exponential growth?

<p>y = a(1 + r)^t where a &gt; 0.</p> Signup and view all the answers

What is the formula for exponential decay?

<p>y = a(1 - r)^t where a &gt; 0.</p> Signup and view all the answers

What is the Compound Interest Formula?

<p>A = P(1 + r/n)^(nt)</p> Signup and view all the answers

What does Pe^rt represent?

<p>Compounded continuously.</p> Signup and view all the answers

What is the logarithm definition?

<p>C = a^b; loga(c) = b.</p> Signup and view all the answers

If there is no base in the log, what is the base?

<ol start="10"> <li></li> </ol> Signup and view all the answers

What is the log product property?

<p>log(b) m + log(b) n = log(b) mn.</p> Signup and view all the answers

What is the log power property?

<p>log(b) m^n = n log(b) m.</p> Signup and view all the answers

What is the quotient property of logarithms?

<p>logb(m/n) = logb m - logb n.</p> Signup and view all the answers

What is the inverse of y = e^x?

<p>y = lnx.</p> Signup and view all the answers

State an alternative form for exponential growth with e.

<p>F(x) = ae^(kt).</p> Signup and view all the answers

State an alternative form for exponential decay with e.

<p>ae^(-kt).</p> Signup and view all the answers

What is a recursive sequence?

<p>A sequence that defines each term using previous terms.</p> Signup and view all the answers

Study Notes

Linear Regression

  • Use the 'stat' menu to find lists and calculate linear regression.
  • Ensure 'stat diagnostic' is enabled for accurate results.

Function

  • A function establishes a unique relationship between each element of the domain and the range.
  • Examples of non-functions include any situation where an input produces multiple outputs.

One-to-One Function

  • Each range element is uniquely paired with a domain element.

Mutually Exclusive Events

  • Events that cannot occur simultaneously, e.g., rolling a 2 and 6 in one die throw.

Extraneous Root

  • A solution that does not satisfy the original equation or problem.

Horizontal Line Test

  • A method to check if a function is one-to-one by assessing if any horizontal line intersects the graph at more than one point.

Vertical Line Test

  • A graphical method to determine whether a curve represents a function.

Set Notation Example

  • Represents a set with criteria, e.g., {x| x>0} defines all positive numbers.

Interval Notation

  • A way to denote ranges, e.g., [ for inclusive and ( for exclusive bounds.

Completing the Square

  • Use the formula (B/2)² = c for transforming quadratics into vertex form.

Axis of Symmetry Formula

  • Given by -b/2a for parabolic functions.

Quadratic Formula

  • Solves quadratic equations: x = (-b ± √(b² - 4ac))/2a.

Vertex Form of a Quadratic

  • Written as y = a(x-h)² + k where (h, k) is the vertex.

Horizontal Shift

  • Represented by the transformation f(x-h).

Vertical Shift

  • Represented by the transformation f(x) + k.

Reflection Over the X-Axis

  • Transformation changes (x, y) to (x, -y), negating the y-values, represented as -f(x).

Reflection Over the Y-Axis

  • Transformation changes (x, y) to (-x, y), represented as f(-x).

Vertical Dilation

  • Changes to a f(x), where a > 1 results in a vertical stretch.

Horizontal Dilation

  • Occurs when b > 1, using the reciprocal x = (1/b)x.

Even Function

  • Defined by the property f(-x) = f(x), indicating symmetry around the y-axis.

Odd Function

  • Defined by the property f(-x) = -f(x), indicating symmetry around the origin.

Conjugate

  • A complex number's conjugate pairs a + bi with a - bi.

Additive Inverse

  • An expression of the form A + bi becomes -A - bi.

Multiplicative Inverse

  • A is replaced by 1/(a + bi), ensuring the imaginary unit i isn't in the denominator.

Finding Quadratic Equation Coefficients

  • Roots relate to coefficients through (R1 + R2) = -B/a and (R1 * R2) = C/a.

Vertical Asymptote

  • Found where the denominator B(x) = 0.

Solving Rational Inequalities

  • Steps include identifying undefined fractions, finding roots, constructing a number line, and determining satisfying values.

Horizontal Asymptote Equation

  • Expressed as Y = a(x)/b(x) based on polynomial degrees.

Horizontal Asymptote Conditions

  • If degree of a(x) > b(x), no asymptote exists; if <, y = 0 is the asymptote; if equal, leading coefficients yield the asymptote value.

Asymptote Transformation

  • Adjusted using the formula (A/x-h) + k.

Exponential Growth Function

  • Described by the formula y = a(1 + r)², where a > 0.

Exponential Decay Function

  • Described by the formula y = a(1 - r)², where a > 0.

Compound Interest Formula

  • A = P(1 + r/n)^(nt), with n representing the number of compounding periods per year.

Continuously Compounded Interest

  • Expressed with Pe^rt, where e is Euler's number.

Logarithms

  • Defined as c = a^b implies loga(c) = b.

Log Base Absence

  • If no base is stated in a logarithm, the base is assumed to be 10.

Logarithmic Product Property

  • logb(m) + logb(n) = logb(mn).

Logarithmic Power Property

  • logb(m^n) = n logb(m).

Quotient Property

  • logb(m/n) = logb(m) - logb(n).

Inverse of y = e^x

  • Inverse function is y = lnx.

Alternative Exponential Growth Model

  • Expressed as F(x) = ae^kt.

Alternative Exponential Decay Model

  • Expressed as ae^(-kt).

Recursive Sequence

  • A sequence where each term is based on the previous term(s) with a defined relationship (not fully detailed).

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Test your knowledge of key concepts in Algebra 2 with these flashcards. Each card provides definitions and explanations for important terms such as linear regression and functions. Master these concepts to excel in your Algebra 2 Regents exam.

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