Algebra 2 Regents Flashcards

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.

False Signup and view all the answers

What is an extraneous root?

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

What is the horizontal line test used for?

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

What does the vertical line test determine?

If a curve is the graph of a function. Signup and view all the answers

Provide an example of set notation.

{x | x > 0} Signup and view all the answers

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

[5, ∞) Signup and view all the answers

How do you complete the square?

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

What is the axis of symmetry formula?

-b/2a Signup and view all the answers

State the quadratic formula.

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

What is the vertex form of a quadratic equation?

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

What represents a horizontal shift in a function?

f(x - h) Signup and view all the answers

What represents a vertical shift in a function?

f(x) + k Signup and view all the answers

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

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

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

(-x, y) Signup and view all the answers

What is vertical dilation?

a * f(x) where a > 1 indicates vertical stretch. Signup and view all the answers

How does horizontal dilation affect a function?

(1/b)(x), y with b > 1. Signup and view all the answers

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

True Signup and view all the answers

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

True Signup and view all the answers

What are conjugates?

(a + bi) and (a - bi) Signup and view all the answers

What is the additive inverse?

A + bi to -a - bi Signup and view all the answers

What is the multiplicative inverse?

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

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

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

What is the vertical asymptote equation?

B(x) = 0 Signup and view all the answers

What is the horizontal asymptote equation?

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

What is the asymptote parent function?

Y = 1/x Signup and view all the answers

How many horizontal asymptotes are there?

More than one. Signup and view all the answers

How do you transform an asymptote?

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

What is the formula for exponential growth?

y = a(1 + r)^t where a > 0. Signup and view all the answers

What is the formula for exponential decay?

y = a(1 - r)^t where a > 0. Signup and view all the answers

What is the Compound Interest Formula?

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

What does Pe^rt represent?

Compounded continuously. Signup and view all the answers

What is the logarithm definition?

C = a^b; loga(c) = b. 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?

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

What is the log power property?

log(b) m^n = n log(b) m. Signup and view all the answers

What is the quotient property of logarithms?

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

What is the inverse of y = e^x?

y = lnx. Signup and view all the answers

State an alternative form for exponential growth with e.

F(x) = ae^(kt). Signup and view all the answers

State an alternative form for exponential decay with e.

ae^(-kt). Signup and view all the answers

What is a recursive sequence?

A sequence that defines each term using previous terms. 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).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

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.