Untitled Quiz

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Questions and Answers

What defines a function?

A relationship that is only represented by equations.

A relationship where the output is always greater than the input.

A relationship in which each element of the domain is paired with exactly one element of the range. (correct)

A relationship where each element of the domain has multiple outputs.

What is the independent variable in a function?

The input or x-value.

What is the dependent variable in a function?

The output or y-value.

What is the domain of a function?

The set of all possible input values (x) of a function. Signup and view all the answers

What is the range of a function?

The set of all possible output values (y) of a function. Signup and view all the answers

What does it mean to evaluate a function?

To find the value of the output for a given input. Signup and view all the answers

Function notation is an inefficient way to write functions in mathematics.

False Signup and view all the answers

What is a constant function?

A function whose output is the same for all inputs. Signup and view all the answers

What is a linear function?

A function whose input is equal to its output. Signup and view all the answers

What is a quadratic function?

A function whose input value is raised to the 2nd power. Signup and view all the answers

What is a cubic function?

A function whose input is raised to the 3rd power. Signup and view all the answers

What is an exponential function?

A function whose base is being raised to a variable power. Signup and view all the answers

The graph of an absolute value function looks like a V.

True Signup and view all the answers

What is discrete data?

Data that can only take certain values. Signup and view all the answers

What is continuous data?

Data that can take any value. Signup and view all the answers

What are transformations in graphing?

Changes to a parent graph. Signup and view all the answers

What is a reflection in graphing transformations?

A type of transformation that flips the graph of a function. Signup and view all the answers

What is a dilation in graphing transformations?

A type of transformation that makes the graph of a function larger or smaller. Signup and view all the answers

What is a horizontal shift in graphing transformations?

A type of transformation that moves a graph left or right. Signup and view all the answers

What is a vertical shift in graphing transformations?

A type of transformation that moves a graph up or down. Signup and view all the answers

Study Notes

Functions

A function pairs each element of the domain (input/x) with one element of the range (output/y).
Functions can be represented using verbal descriptions, tables, graphs, or equations.

Variables

Independent Variable: The input or x-value of a function.
Dependent Variable: The output or y-value that relies on the input.

Function Characteristics

Domain: All possible input values (x) for a function.
Range: All possible output values (y) for a function.

Evaluation and Notation

Evaluate: Process to find the output value for a specified input.
Function Notation: Written as f(x) instead of y, representing functions in a concise manner.

Parts of an Equation

Variable: A symbol (typically a letter) representing a number.
Coefficient: A number multiplied by a variable.
Constant: A number that remains unchanged.
Operator: Symbol indicating mathematical operations (addition, subtraction, etc.).
Exponent (Power): Indicates how many times a base is multiplied by itself.

Types of Functions

Parent Function: The simplest form of a function from which other functions are derived.
Constant Function: Maintains the same output regardless of input; represented as a horizontal line.
Linear Function: Relationship where input equals output; represented as y = x.
Quadratic Function: Involves the square of the input; produces a U-shaped graph known as a parabola (y = x²).
Cubic Function: Involves the cube of the input.
Square Root Function: Derives output from the square root of the input, undefined for negative values.
Absolute Value Function: Measures distance from zero; graph appears as a V shape (y = |x|).
Exponential Function: Base raised to a variable power, with the input as the exponent.
Rational Function: Involves fractions; undefined for an input of zero (cannot divide by zero).

Graphing Concepts

Graph: A representation of ordered pairs (input/output values) forming a line or curve on the coordinate plane.
Ordered Pair: A duo of numbers that identifies a point on the coordinate plane.
Coordinate Plane: Divided into four quadrants by the x-axis (horizontal) and y-axis (vertical).

Data Types

Discrete Data: Can only take specific values; for example, counting items like the number of students.
Continuous Data: Can take any value within a range; for example, heights of individuals.

Transformations

Alterations to a parent graph include:
- Reflection: Flips the graph across a line.
- Dilation: Changes the size of the graph, either enlarging or shrinking.
- Horizontal Shift: Moves the graph left or right.
- Vertical Shift: Moves the graph up or down.