Questions and Answers
What is an absolute value function?
An absolute value function is a function that contains an algebraic expression within absolute value symbols.
What is end behavior in the context of a function?
The behavior of the graph of a function as x approaches positive infinity or negative infinity.
What are extrema?
The maximum and minimum values of a function.
What is a one-to-one function?
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What is an onto function?
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What is a piecewise-linear function?
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What characterizes a step function?
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What does the vertical line test determine?
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What is the zero of a function?
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What does it mean if a relation is not a function?
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What is the standard form of a quadratic function?
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What is the standard form of a cubic function?
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What is a rational function?
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What is an exponential function?
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What is the standard form of a logarithmic function?
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What is the equation of a square root function?
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Study Notes
Function Types and Characteristics
- Absolute Value Function: Contains an algebraic expression enclosed within absolute value symbols, yielding non-negative outputs.
- End Behavior: Refers to the trends of a function's graph as the input variable (x) approaches positive or negative infinity.
- Extrema: Represents the highest (maximum) and lowest (minimum) values that a function can achieve, crucial in optimization.
- One-to-One Function: A function where each input (domain) corresponds to precisely one unique output (range), ensuring no repeated outputs.
- Onto Function: Implies that every output in the range has a corresponding input in the domain, covering all possible outputs.
- Piecewise-Linear Function: Composed of various linear equations defined over different intervals, creating distinct pieces on its graph.
- Step Function: Features a graph that resembles a series of connected line segments, resembling a staircase.
- Vertical Line Test: A method to determine if a relation is a function; if a vertical line intersects the graph at most once, it qualifies as a function.
Function Zeroes and Types
- Zero of a Function: Identifies the input value (x) that results in an output of zero from the function (f(x)=0).
- Not a Function: Describes a situation where the output directly inverses the input, breaking the definition of a function.
- Quadratic Function: Expressed in the form f(x) = ax² + bx + c, characterized by a parabolic graph, with 'a' being non-zero.
- Cubic Function: Defined by the equation f(x) = x³, featuring a graph that can exhibit one or two turning points and can extend to positive or negative infinity.
- Rational Function: Composed of two parabolas and asymptotes, which are lines that the graph approaches but never touches.
- Exponential Function: Characterized by the equation y = ab^x, where 'a' is a non-zero constant and 'b' is the base of the exponential function.
- Logarithmic Function: Described as f(x) = log_b(x) where base 'b' is positive and not equal to one; serves as the inverse to the exponential function f(x) = b^x.
- Square Root Function: Expressed as f(x) = √x, with a domain of [0, ∞) and range of [0, ∞), displaying a gradually increasing curve starting from the origin.
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Description
Explore key concepts related to functions in Algebra 2 with these informative flashcards. Each card defines important terms such as absolute value functions, end behavior, and extrema. Perfect for mastering the foundational elements of algebraic functions.
