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.
Signup and view all the answers
What is an extraneous root?
Signup and view all the answers
What is the horizontal line test used for?
Signup and view all the answers
What does the vertical line test determine?
Signup and view all the answers
Provide an example of set notation.
Signup and view all the answers
What is interval notation for '5 greater than or equal to x'?
Signup and view all the answers
How do you complete the square?
Signup and view all the answers
What is the axis of symmetry formula?
Signup and view all the answers
State the quadratic formula.
Signup and view all the answers
What is the vertex form of a quadratic equation?
Signup and view all the answers
What represents a horizontal shift in a function?
Signup and view all the answers
What represents a vertical shift in a function?
Signup and view all the answers
How do you reflect a function over the x-axis?
Signup and view all the answers
How do you reflect a function over the y-axis?
Signup and view all the answers
What is vertical dilation?
Signup and view all the answers
How does horizontal dilation affect a function?
Signup and view all the answers
An even function satisfies f(-x) = f(x).
Signup and view all the answers
An odd function satisfies f(-x) = -f(x).
Signup and view all the answers
What are conjugates?
Signup and view all the answers
What is the additive inverse?
Signup and view all the answers
What is the multiplicative inverse?
Signup and view all the answers
How do you find the quadratic equation's a, b, and c with roots?
Signup and view all the answers
What is the vertical asymptote equation?
Signup and view all the answers
What is the horizontal asymptote equation?
Signup and view all the answers
What is the asymptote parent function?
Signup and view all the answers
How many horizontal asymptotes are there?
Signup and view all the answers
How do you transform an asymptote?
Signup and view all the answers
What is the formula for exponential growth?
Signup and view all the answers
What is the formula for exponential decay?
Signup and view all the answers
What is the Compound Interest Formula?
Signup and view all the answers
What does Pe^rt represent?
Signup and view all the answers
What is the logarithm definition?
Signup and view all the answers
If there is no base in the log, what is the base?
Signup and view all the answers
What is the log product property?
Signup and view all the answers
What is the log power property?
Signup and view all the answers
What is the quotient property of logarithms?
Signup and view all the answers
What is the inverse of y = e^x?
Signup and view all the answers
State an alternative form for exponential growth with e.
Signup and view all the answers
State an alternative form for exponential decay with e.
Signup and view all the answers
What is a recursive sequence?
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.