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Questions and Answers
What is the correct form of a linear equation in two variables?
What is the correct form of a linear equation in two variables?
- ax^2 + by^2 = c
- ax + by^2 = c
- ax - by = c
- ax + by = c (correct)
Which of the following is NOT a method for solving systems of equations?
Which of the following is NOT a method for solving systems of equations?
- Graphing
- Substitution
- Elimination
- Synthesis (correct)
What is the range of the function f(x) = 2x^2 + 3x - 4?
What is the range of the function f(x) = 2x^2 + 3x - 4?
- All real numbers (correct)
- All negative real numbers
- All positive real numbers
- No real numbers
What is the slope-intercept form of a linear equation?
What is the slope-intercept form of a linear equation?
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Which of the following is an example of an inequality?
Which of the following is an example of an inequality?
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What is the x-intercept of the graph of the equation y = 2x - 3?
What is the x-intercept of the graph of the equation y = 2x - 3?
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What is the composition of functions f(x) = 2x and g(x) = x^2?
What is the composition of functions f(x) = 2x and g(x) = x^2?
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What is the graph of the equation x = 2 a vertical or horizontal line?
What is the graph of the equation x = 2 a vertical or horizontal line?
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Study Notes
Equations
- An equation is a statement that says two expressions are equal.
- Equations can be linear (degree 1) or nonlinear (degree 2 or higher).
- Linear equations can be written in the form:
ax + by = c, wherea,b, andcare constants. - Equations can be solved using various methods, including:
- Addition and subtraction
- Multiplication and division
- Substitution
- Elimination
Inequalities
- An inequality is a statement that says two expressions are not equal.
- Inequalities can be linear or nonlinear.
- Linear inequalities can be written in the form:
ax + by > c,ax + by < c,ax + by ≥ c, orax + by ≤ c. - Inequalities can be solved using various methods, including:
- Graphing on a number line
- Testing points
- Solving related equations
Functions
- A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
- Functions can be represented algebraically, graphically, or numerically.
- Function notation:
f(x) = ...ory = ... - Key concepts:
- Domain and range
- Function operations (addition, subtraction, multiplication, division)
- Composition of functions
Systems of Equations
- A system of equations is a set of two or more equations with two or more variables.
- Systems can be solved using various methods, including:
- Substitution
- Elimination
- Graphing
- Types of systems:
- Independent systems (unique solution)
- Dependent systems (infinite solutions)
- Inconsistent systems (no solution)
Graphing
- Graphing is a visual representation of equations and functions on a coordinate plane.
- Key concepts:
- x-axis (horizontal) and y-axis (vertical)
- Quadrants (I, II, III, IV)
- Intercepts (x-intercept, y-intercept)
- Slope and steepness
- Graphing methods:
- Plotting points
- Using slope-intercept form (y = mx + b)
- Using standard form (Ax + By = C)
Equations
- Equations are statements that express the equality of two expressions.
- They can be classified as linear (degree 1) or nonlinear (degree 2 or higher).
- Linear equations can be written in the form
ax + by = c, wherea,b, andcare constants. - Various methods can be used to solve equations, including:
- Addition and subtraction
- Multiplication and division
- Substitution
- Elimination
Inequalities
- Inequalities are statements that express the non-equality of two expressions.
- Like equations, they can be linear or nonlinear.
- Linear inequalities can be written in the form
ax + by > c,ax + by < c,ax + by ≥ c, orax + by ≤ c. - Inequalities can be solved using various methods, including:
- Graphing on a number line
- Testing points
- Solving related equations
Functions
- Functions are relations between a set of inputs (domain) and a set of possible outputs (range).
- They can be represented algebraically, graphically, or numerically.
- Function notation:
f(x) =...ory =.... - Key concepts:
- Domain and range
- Function operations (addition, subtraction, multiplication, division)
- Composition of functions
Systems of Equations
- Systems of equations consist of two or more equations with two or more variables.
- Systems can be solved using various methods, including:
- Substitution
- Elimination
- Graphing
- Types of systems:
- Independent systems (unique solution)
- Dependent systems (infinite solutions)
- Inconsistent systems (no solution)
Graphing
- Graphing is a visual representation of equations and functions on a coordinate plane.
- Key concepts:
- x-axis (horizontal) and y-axis (vertical)
- Quadrants (I, II, III, IV)
- Intercepts (x-intercept, y-intercept)
- Slope and steepness
- Graphing methods:
- Plotting points
- Using slope-intercept form (y = mx + b)
- Using standard form (Ax + By = C)
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