Algebra 2 EOC Flashcards

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Questions and Answers

What is a relation?

  • A graphical representation of data
  • A set of ordered pairs (correct)
  • A set of unordered pairs
  • A set of numbers

What is the domain of a relation?

X-coordinates input

What is the range of a relation?

Y-coordinates output

In a function, all x's can be the same.

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

What is the formula for direct variation?

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

What is the formula for inverse variation?

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

What is joint variation?

<p>Y varies jointly with x and z</p> Signup and view all the answers

What is a horizontal asymptote for rational expressions?

<p>No horizontal asymptote</p> Signup and view all the answers

How do you find a vertical asymptote?

<p>Set denominator equal to zero and factor</p> Signup and view all the answers

What do you do to find x-intercepts for rational expressions?

<p>Divide out any common denominator</p> Signup and view all the answers

How do you factor a sum or difference of cubes?

<p>First one second one squared</p> Signup and view all the answers

What is the formula for continuous compounding?

<p>A=Pe^(rt)</p> Signup and view all the answers

What is the square root of -1?

<p>I</p> Signup and view all the answers

What is i^2?

<p>-1</p> Signup and view all the answers

What does the rational exponent mean?

<p>Power/root='power over root'</p> Signup and view all the answers

How do you find the inverse of a function?

<p>'Y=' form switch x and y solve for y</p> Signup and view all the answers

How do you solve an absolute value equation?

<p>Set the expression inside the absolute value equal to the positive and negative constants</p> Signup and view all the answers

What ways can you solve a system?

<p>Graph (A), Combination (B), Substitution (D)</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 is the standard form for a quadratic?

<p>F(x)=ax^2+bx+c</p> Signup and view all the answers

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Study Notes

Key Algebra 2 Concepts

  • Relation: Refers to a set of ordered pairs, linking elements from one set to another.

  • Domain: The set of all x-coordinates (inputs) in a relation or function.

  • Range: The set of all y-coordinates (outputs) in a relation or function.

  • Function: A specific type of relation where each x-coordinate is unique; passes the vertical line test.

Variation Types

  • Direct Variation: Expressed mathematically as ( Y = kx ), where ( k ) is a non-zero constant.

  • Inverse Variation: Represented by ( Y = \frac{k}{x} ), indicating that y varies inversely with x.

  • Joint Variation: A scenario where y varies jointly with multiple variables, such as ( x ) and ( z ).

Asymptotes in Rational Functions

  • Horizontal Asymptote: Indicates that a rational expression has no horizontal asymptote when its degree is higher in the numerator than the denominator.

  • Vertical Asymptote: Found by setting the denominator equal to zero and factoring.

Rational Expressions

  • X-Intercepts for Rational Expressions: These can be determined by dividing out any common denominators.

Factoring Techniques

  • Sum or Difference of Cubes: Factorable using the formula ( a^3 \pm b^3 = (a \pm b)(a^2 \mp ab + b^2) ).

Advanced Formulas

  • Continuous Compounding: Described by the formula ( A = Pe^{(rt)} ), where ( A ) is the amount, ( P ) is the principal, ( r ) is the rate, and ( t ) is time.

  • Compound Interest Formula: Given by ( A = P(1+\frac{r}{n})^{(nt)} ), where ( n ) is the number of times interest is compounded per year.

Complex Numbers

  • Square Root of -1: Denoted as ( i ), the imaginary unit.

  • Definition of ( i^2 ): By definition, ( i^2 = -1 ).

Exponents and Inverses

  • Rational Exponent Meaning: Represents "power over root", indicating the relationship between exponents and roots.

  • Finding Inverse of a Function: To find the inverse, switch ( x ) and ( y ) in the equation and solve for ( y ).

Solving Equations

  • Absolute Value Equations: Solved by setting the expression inside the absolute value equal to both the positive and negative constants.

Systems of Equations

  • Methods to Solve Systems: Include graphing, substitution, combinations, and elimination methods.

Quadratic Function Form

  • Standard Form for Quadratic: The equation format is ( f(x) = ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants.

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