Algebra Class: Functions and Their Properties

Questions and Answers

What is a parent function?

The simplest function of a family of functions (correct)

A complex mathematical operation

A function with multiple variables

None of the above

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?

A function of the form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to zero. Signup and view all the answers

What is an absolute value function?

A function that contains an algebraic expression within absolute value symbols. Signup and view all the answers

What is a rational function?

A function that has two graphs (parabolas) and asymptotes. Signup and view all the answers

What is an x-intercept?

Where the graph crosses the x-axis. Signup and view all the answers

What is a y-intercept?

Where the line crosses the y-axis. Signup and view all the answers

What does it mean when a function is increasing?

Becoming greater or larger. Signup and view all the answers

What does it mean when a function is decreasing?

The graph of a function goes down on a portion of its domain when viewed from left to right. Signup and view all the answers

What is the minimum of a function?

The smallest value of the function. Signup and view all the answers

What is an equation?

A mathematical sentence that contains an equals sign. Signup and view all the answers

What is the domain of a function?

The complete set of possible values of the independent variable. Signup and view all the answers

What is range in mathematics?

The difference between the highest and lowest scores in a distribution. Signup and view all the answers

What is input in terms of functions?

Something put into a system to achieve a result. Signup and view all the answers

What is output in a function?

The results of the operation of any system. Signup and view all the answers

What is an asymptote?

A line that a graph approaches but never crosses. Signup and view all the answers

What does it mean when a graph opens upward?

The graph has a minimum. Signup and view all the answers

What does it mean when a graph opens downward?

The graph has a maximum. Signup and view all the answers

What is infinity?

Endless or unlimited space, time, or distance. Signup and view all the answers

What is an expression in mathematics?

A mathematical phrase that contains operations, numbers, and/or variables. Signup and view all the answers

What is a polynomial?

An expression consisting of variables and coefficients, involving addition, subtraction, multiplication, and non-negative integer exponents. Signup and view all the answers

What is an even function?

A function symmetric with respect to the y-axis; f(x) = f(-x). Signup and view all the answers

What is an odd function?

A function symmetric with respect to the origin; f(-x) = -f(x). Signup and view all the answers

What is a point of intersection?

A point that two graphs have in common. Signup and view all the answers

What are endpoints in geometry?

Points on the ends of line segments. Signup and view all the answers

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.