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Questions and Answers
What does the domain of a function represent?
What does the domain of a function represent?
- The set of all output values.
- The relationship between input and output values.
- The set of all input values. (correct)
- The maximum value of the function.
Which of these equations could determine the slope of a line?
Which of these equations could determine the slope of a line?
- $y = bx + a^2$
- $x = ky + c$
- $y = mx + b$ (correct)
- $y - y_1 = m(x - x_1)$ (correct)
What is true about parallel lines in terms of slope?
What is true about parallel lines in terms of slope?
- Their slopes are both zero.
- They have different slopes.
- They have the same slope. (correct)
- They intersect at a right angle.
Which formula would you use to calculate the distance between two points in a coordinate plane?
Which formula would you use to calculate the distance between two points in a coordinate plane?
What does a negative slope in a linear equation indicate?
What does a negative slope in a linear equation indicate?
Flashcards
Functions and Relations
Functions and Relations
A relationship where each input has exactly one output.
Domain
Domain
The set of possible input values (x-values) in a relationship.
Range
Range
The set of possible output values (y-values) in a relationship.
Slope
Slope
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Parallel Lines
Parallel Lines
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Study Notes
Functions and Relations
- A set is a collection of unique objects.
- An element is an object in a set.
- A relation associates elements in one set with elements of another.
- A way to represent a set is listing its elements within curly brackets { }.
- The set of first elements in a relation is called the domain, representing input values.
- The set of related second elements in a relation is called the range, representing output values.
- Functions are a special type of relation where each element in the domain is associated with exactly one element in the range.
- A graph represents a function when no two points lie on the same vertical line.
- Function notation, d(t), defines a function named d.
- Input is independent, expressed by x or t.
- Output is dependent, expressed by y or d.
- A linear equation is expressed as y = mx + b, where m is the rate of change (slope), and b is the y-intercept.
Domain and Range
- The domain of a function is the set of all possible input values (x-values).
- The range of a function is the set of all possible output values (y-values), often listed in order.
- Discrete graphs have unconnected points, while continuous graphs are unbroken.
- To describe the domain and range, use inequalities or interval notation.
Holes in the Graph
- A hole in a graph indicates a point where the function does not exist.
- The domain and range may be limited by holes.
- The domain and range are described using inequalities or interval notation (e.g., (-∞, 3) U (3, ∞)).
Vertical Line Test
- A graph represents a function if any vertical line drawn on the graph intersects the graph at most once.
Lines and Graphing
- The general equation of a line is y = mx + b, where:
- y represents the dependent variable (output).
- x represents the independent variable (input).
- m represents the rate of change (slope).
- b represents the y-intercept (the value of y when x = 0).
Midpoint
- The midpoint between two points (x₁, y₁) and (x₂, y₂) is calculated by averaging the x- coordinates and the y-coordinates:
- Midpoint = ((x₁ + x₂)/2), ((y₁ + y₂)/2)).
Distance Between Two Points
- The distance between two points (x₁, y₁) and (x₂, y₂) is calculated using the distance formula:
- Distance = √((x₂ - x₁)² + (y₂ - y₁)²).
Slopes of Parallel and Perpendicular Lines
- Parallel lines have the same slope.
- Perpendicular lines have negative reciprocal slopes (the product of their slopes is -1).
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