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# Thinkwell Algebra 2 Chapter 1.2 Flashcards

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@AmicableNeodymium

### What is a relation?

• A set of ordered pairs (x,y) (correct)
• A function of two variables
• A set of x-values only
• A single ordered pair
• ### What is the domain in a relation?

The set of all of the possible x-values (inputs).

### What does the range refer to in a relation?

The set of all the possible y-values (outputs).

### What defines a function?

<p>A relation where each input (x, domain) has exactly one output (y, range).</p> Signup and view all the answers

### The Vertical Line Test (VLT) determines if a relation is a function.

<p>True</p> Signup and view all the answers

### What is the independent variable in a function?

<p>The input of a function (x).</p> Signup and view all the answers

### What is a dependent variable?

<p>A variable whose value depends on that of another (the input, often denoted by y).</p> Signup and view all the answers

### What does the function notation f(x) represent?

<p>It is the same as Y; plug in the number into x and simplify.</p> Signup and view all the answers

### What is a transformation in geometry?

<p>A change in the position, size, or shape of a figure.</p> Signup and view all the answers

### Name the four types of transformations.

<p>Reflection, translation, rotation, dilation.</p> Signup and view all the answers

### What is an image in relation to transformations?

<p>A shape that results from a transformation of a figure.</p> Signup and view all the answers

### What is the preimage of a transformation?

<p>The original figure prior to a transformation.</p> Signup and view all the answers

### What is reflection in geometric transformations?

<p>A transformation across a line, called the line of reflection, resulting in a mirror image.</p> Signup and view all the answers

### What does translation describe in transformations?

<p>A transformation that 'slides' each point of a figure the same distance in the same direction.</p> Signup and view all the answers

### What is a rotation in geometry?

<p>Circular movement around an axis; distance from the center always stays the same.</p> Signup and view all the answers

### What is dilation in geometric transformations?

<p>A transformation that changes the size of an object but not the shape.</p> Signup and view all the answers

### What do compression functions do?

<p>Make the graph more narrow.</p> Signup and view all the answers

### What is the effect of stretch functions on a graph?

<p>They widen the graph.</p> Signup and view all the answers

### What occurs during vertical compression?

<p>The graph gets shorter and moves towards the x-axis.</p> Signup and view all the answers

### What happens during a vertical stretch?

<p>The graph moves up or down the y-axis and gets taller.</p> Signup and view all the answers

### What does horizontal compression do to a graph?

<p>It squeezes the graph towards the y-axis.</p> Signup and view all the answers

### What is the effect of a horizontal stretch on a graph?

<p>The graph gets shorter and wider.</p> Signup and view all the answers

### What is a parent function?

<p>The most basic function of a family of functions.</p> Signup and view all the answers

### What is the constant parent function?

<p>f(x) = c</p> Signup and view all the answers

### What is the linear parent function?

<p>y = x or f(x) = x.</p> Signup and view all the answers

### What is the quadratic parent function?

<p>f(x) = x^2 or y = x^2.</p> Signup and view all the answers

### What is the cubic parent function?

<p>f(x) = x^3 or y = x^3.</p> Signup and view all the answers

### What is the square root parent function?

<p>f(x) = √x.</p> Signup and view all the answers

### What is rotation in terms of transformations?

Signup and view all the answers

### What is reflection in transformations?

Signup and view all the answers

### What does translation refer to in transformations?

Signup and view all the answers

## Study Notes

### Relations and Functions

• A relation is defined as a set of ordered pairs (x,y), representing inputs and outputs.
• The domain consists of all possible x-values (inputs) in a relation.
• The range includes all possible y-values (outputs) from a relation.
• A function is a specific type of relation where each input corresponds to exactly one output.

### Identifying Functions

• The Vertical Line Test (VLT) determines if a relation is a function; if a vertical line intersects the graph at more than one point, the relation is not a function.

### Variables in Functions

• The independent variable (x) is the input that influences the output.
• The dependent variable (y) is the output that depends on the input.

### Function Notation

• Function Notation (f(x)) represents the output of a function in terms of its input. It can be used to simplify expressions by substituting values into x.

### Transformations

• A transformation alters a figure's position, size, or shape.
• Four primary types of transformations include:
• Reflection: A mirrored image across a specific line.
• Translation: A slide of the figure in a particular direction.
• Rotation: Circular movement around a fixed point, keeping equal distance from the center.
• Dilation: Adjusts the size while maintaining the shape.

### Compression and Stretching

• Compression functions narrow the graph, pulling it towards the axis.
• Stretch functions widen the graph, pushing it away from the axis.

### Vertical Transformations

• Vertical Compression: Shrinks the graph towards the x-axis by reducing y-values (multiplying by a factor less than 1).
• Vertical Stretch: Expands the graph upwards by increasing y-values (multiplying by a factor greater than 1).

### Horizontal Transformations

• Horizontal Compression: Squeezes the graph toward the y-axis, reducing x-values (multiplying x by a factor greater than 1).
• Horizontal Stretch: Expands the graph sideways, increasing x-values (multiplying x by a fraction).

### Parent Functions

• The parent function is the simplest form of a function before any transformations.
• Constant Parent Function: f(x) = c
• Linear Parent Function: f(x) = x
• Quadratic Parent Function: f(x) = x²
• Cubic Parent Function: f(x) = x³
• Square Root Parent Function: f(x) = √x

• An image refers to the resulting shape after a transformation.
• The preimage is the original figure before any transformation is applied.

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## Description

Test your knowledge of key concepts in Algebra 2 with these flashcards from Chapter 1.2. This includes important terms like relation, domain, range, and function. Each term is defined to enhance your understanding of functions and their properties.

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