Questions and Answers
What is the set of input values in a function?
What is the property of real numbers that states a + b = b + a?
What is the process of combining like terms in an algebraic expression?
What type of function has the general form f(x) = mx + b?
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What is the trigonometric ratio of the opposite side to the hypotenuse?
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What is the equation for the Pythagorean Identity?
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What is the first step in solving a linear equation?
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What is the xintercept of a linear function?
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What is the trigonometric ratio of the adjacent side to the hypotenuse?
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What is the correct order of operations?
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Study Notes
Numbers and Operations
 Real Numbers: Include all rational and irrational numbers, can be represented on the number line

Properties of Real Numbers:
 Commutative Property: a + b = b + a, ab = ba
 Associative Property: (a + b) + c = a + (b + c), (ab)c = a(bc)
 Distributive Property: a(b + c) = ab + ac
 Order of Operations: Follow the order of parentheses, exponents, multiplication and division, and addition and subtraction
Algebraic Expressions and Equations
 Expressions: A collection of variables, constants, and algebraic operations
 Equations: Two expressions equal to each other

Simplifying Expressions:
 Combine like terms
 Use the distributive property
 Use the properties of real numbers

Solving Linear Equations:
 Add, subtract, multiply, or divide both sides by the same value
 Use inverse operations to isolate the variable
Functions
 Domain and Range: Domain is the set of input values, range is the set of output values
 Function Notation: f(x) = output value, where x is the input value

Types of Functions:
 Linear Functions: f(x) = mx + b, where m is the slope and b is the yintercept
 Quadratic Functions: f(x) = ax^2 + bx + c, where a, b, and c are constants

Graphing Functions:
 Use the xaxis for the domain and the yaxis for the range
 Identify the xintercept(s) and yintercept
Trigonometry

Angles and Triangles:
 Degrees, minutes, and seconds
 Right triangles, acute angles, and obtuse angles

Trigonometric Ratios:
 Sine (sin), cosine (cos), and tangent (tan)
 sin(A) = opposite side / hypotenuse, cos(A) = adjacent side / hypotenuse, tan(A) = opposite side / adjacent side

Identities and Formulas:
 Pythagorean Identity: sin^2(A) + cos^2(A) = 1
 Sum and Difference Formulas: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), etc.
Analytic Geometry

Coordinate Plane:
 Quadrants, xaxis, yaxis, and origin
 Plotting points and graphing equations

Circle Equations:
 Standard form: (x  h)^2 + (y  k)^2 = r^2, where (h, k) is the center and r is the radius
 General form: x^2 + y^2 + Dx + Ey + F = 0

Conic Sections:
 Parabolas, ellipses, and hyperbolas
 Equations and graphs of each
Numbers and Operations
 Real numbers include all rational and irrational numbers and can be represented on the number line.
 The Commutative Property of Real Numbers states that the order of numbers does not change the result: a + b = b + a, ab = ba.
 The Associative Property of Real Numbers states that the order in which numbers are grouped does not change the result: (a + b) + c = a + (b + c), (ab)c = a(bc).
 The Distributive Property of Real Numbers states that multiplication can be distributed over addition: a(b + c) = ab + ac.
 The Order of Operations follows the order of parentheses, exponents, multiplication and division, and addition and subtraction.
Algebraic Expressions and Equations
 An algebraic expression is a collection of variables, constants, and algebraic operations.
 An equation is two expressions equal to each other.
 To simplify expressions, combine like terms, use the distributive property, and use the properties of real numbers.
 To solve linear equations, add, subtract, multiply, or divide both sides by the same value, and use inverse operations to isolate the variable.
Functions
 The domain of a function is the set of input values, and the range is the set of output values.
 Function notation is f(x) = output value, where x is the input value.
 Linear functions have the form f(x) = mx + b, where m is the slope and b is the yintercept.
 Quadratic functions have the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
 To graph functions, use the xaxis for the domain and the yaxis for the range, and identify the xintercept(s) and yintercept.
Trigonometry
 Angles can be measured in degrees, minutes, and seconds.
 Right triangles have acute angles and obtuse angles.
 The sine, cosine, and tangent ratios are defined as sin(A) = opposite side / hypotenuse, cos(A) = adjacent side / hypotenuse, and tan(A) = opposite side / adjacent side.
 The Pythagorean Identity states that sin^2(A) + cos^2(A) = 1.
 The Sum and Difference Formulas include sin(A + B) = sin(A)cos(B) + cos(A)sin(B), etc.
Analytic Geometry
 The coordinate plane has four quadrants, an xaxis, a yaxis, and an origin.
 Points can be plotted and equations can be graphed on the coordinate plane.
 Circle equations can be written in standard form: (x  h)^2 + (y  k)^2 = r^2, where (h, k) is the center and r is the radius.
 Circle equations can also be written in general form: x^2 + y^2 + Dx + Ey + F = 0.
 Conic sections include parabolas, ellipses, and hyperbolas, each with its own equation and graph.
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Description
Understand real numbers, properties of real numbers, and order of operations. Also, learn about algebraic expressions and equations.