Functions and Representations flashcards

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What does input-output relations mean?Relations and Functions: A set of input-output pairs.
What is an ordered pair?Relations and Functions: A pair (input, output) in a stated order.
How would you define function rule?Relations and Functions: A mapping with one output per input.
Can two inputs lead to the same output?Relations and Functions: Yes, a function may repeat outputs.
What is meant by vertical line test?Relations and Functions: A graphical check for multiple outputs at one input.
Why does a vertical line reveal a failure?Relations and Functions: Its intersections share an x-coordinate but have different y-coordinates.
What does domain mean?Domain and Range: The set of allowed input values.
Why exclude a denominator zero?Domain and Range: Division by zero is undefined.
How would you define range?Domain and Range: The set of attained output values.
What is the range of x² over real x?Domain and Range: All nonnegative real numbers.
What is meant by contextual restrictions?Domain and Range: A restriction imposed by real-world meaning.
Why may negative time be excluded?Domain and Range: Elapsed time is nonnegative in that model.
What does evaluating f(x) mean?Function Notation: The output of a named function for a stated input.
Does f(3) mean 3f?Function Notation: No, it names the output at input 3.
How would you define solving f(x)=k?Function Notation: An inverse-image question for a specified output.
Why check the domain?Function Notation: Algebraic candidates may not be allowed inputs.
What is meant by function composition?Function Notation: Feeding one function output into another function.
Is f(g(x)) always g(f(x))?Function Notation: No, the two orders can differ.
What does tables mean?Tables, Graphs, and Equations: A list of matching inputs and outputs.
Does a short table prove a unique rule?Tables, Graphs, and Equations: No, multiple rules can fit finitely many points.
How would you define graphs?Tables, Graphs, and Equations: A visual display of coordinate pairs.
Why label axes with units?Tables, Graphs, and Equations: It makes the plotted quantities interpretable.
What is meant by equivalent representations?Tables, Graphs, and Equations: Different displays of one mathematical relationship.
How can a table be checked against an equation?Tables, Graphs, and Equations: Substitute each row into the rule.
What does common difference mean?Arithmetic Sequences: The fixed change between consecutive terms.
What can a negative common difference mean?Arithmetic Sequences: The terms decrease at a constant step.
How would you define explicit rule?Arithmetic Sequences: A formula for the term at position n.
Why subtract one from n?Arithmetic Sequences: The first term is zero steps after itself.
What is meant by recursive rule?Arithmetic Sequences: A next-term rule using a previous term.
What does a recursive rule require?Arithmetic Sequences: An initial term to start the sequence.