Questions and Answers
What is a parent function?
What is an exponential function?
A function whose value is a constant raised to the power of the argument.
What is a linear function?
A function in which the graph of the solutions forms a line.
What is a quadratic function?
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What is an absolute value function?
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What is a rational function?
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What is an x-intercept?
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What is a y-intercept?
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What does it mean when a function is increasing?
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What does it mean when a function is decreasing?
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What is the minimum of a function?
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What is an equation?
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What is the domain of a function?
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What is range in mathematics?
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What is input in terms of functions?
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What is output in a function?
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What is an asymptote?
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What does it mean when a graph opens upward?
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What does it mean when a graph opens downward?
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What is infinity?
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What is an expression in mathematics?
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What is a polynomial?
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What is an even function?
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What is an odd function?
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What is a point of intersection?
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What are endpoints in geometry?
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Study Notes
Parent Function
- Simplest function of a family; serves as a template for other functions.
- For quadratic functions, the parent function is ( y = x^2 ).
- Graph of ( y = x^2 ) is a parabola.
Exponential Function
- Form where the value is a constant raised to the power of the argument.
Linear Function
- A function whose solutions graph as a straight line.
Quadratic Function
- Defined by the standard form ( f(x) = ax^2 + bx + c ) with ( a \neq 0 ).
- The graph forms a parabola, which can open upwards or downwards.
Absolute Value Function
- Contains an algebraic expression in absolute value symbols.
- Graph features a vertex and a line of symmetry.
Rational Function
- Features two graphs (parabolas) and asymptotes, which are lines the graph approaches but never touches.
X-Intercept
- The point at which a graph crosses the x-axis.
Y-Intercept
- The point at which a graph crosses the y-axis.
Increasing Function
- A function where output values grow larger over a given interval.
Decreasing Function
- A function where output values diminish when viewed from left to right along the graph.
Minimum
- The smallest value of a function, known as a local minimum or global minimum depending on the range.
Equation
- A mathematical statement asserting the equality of two expressions, indicated by an equals sign.
Domain
- Set of all possible values of the independent variable (x-values) that produce real y-values.
Range
- Differences between the highest and lowest values in a distribution.
Input
- Elements inserted into a system for a specific outcome.
Output
- The results produced by a system's operations.
Asymptote
- A line that a graph approaches indefinitely without intersecting.
Opens Upward
- A characteristic of a parabola with a minimum point.
Opens Downward
- A characteristic of a parabola with a maximum point.
Infinity
- Refers to endless or limitless aspects relating to space, time, or distance.
Expression
- A combination of numbers, variables, and operations without an equals sign.
Polynomial
- An algebraic expression involving variables and coefficients, featuring addition, subtraction, multiplication, and non-negative integer exponents.
Even Function
- A function whose graph is symmetric about the y-axis, satisfies ( f(x) = f(-x) ).
Odd Function
- A function whose graph is symmetric about the origin, satisfies ( f(-x) = -f(x) ).
Point of Intersection
- A location where two graphs meet or share common coordinates.
Endpoints
- Term for the terminal points on the ends of line segments.
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Description
This quiz covers various types of functions, including parent, exponential, linear, quadratic, absolute value, and rational functions. Understand their general characteristics, graphs, and intercepts. Test your knowledge of function properties and definitions in algebra.