Algebra 2 Unit 2 Flashcards

Questions and Answers

What is the absolute value function?

f(x) = |mx + b| + c (correct)

f(x) = |x| + c

f(x) = mx + b

f(x) = mx^2 + b

What does the axis of symmetry do?

It divides a figure into two parts that are mirror images.

What is the definition of a boundary?

A line in the coordinate plane that separates solutions of an inequality from nonsolutions.

What is the constant of variation?

The ratio of two variables in direct variation. Signup and view all the answers

What does correlation indicate?

The strength of the relationship between two data sets. Signup and view all the answers

What is the correlation coefficient?

It indicates the strength of the correlation. Signup and view all the answers

What does the dependent variable represent?

It represents the output or result in a function. Signup and view all the answers

What is direct variation?

A relationship between two variables where one is a constant multiple of the other. Signup and view all the answers

Define domain.

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

What is function notation?

A way to represent functions using symbols like f(x). Signup and view all the answers

What does the function rule determine?

The relationship between input and output values of a function. Signup and view all the answers

What is a half-plane?

A region of the coordinate plane divided by a line. Signup and view all the answers

Define independent variable.

The variable that represents input values for a function. Signup and view all the answers

What is a line of best fit?

A line that best represents the data on a scatter plot. Signup and view all the answers

What is a linear equation?

An equation whose graph forms a straight line. Signup and view all the answers

What is a linear function?

A function that creates a straight line when graphed. Signup and view all the answers

What is a linear inequality?

An inequality that represents a linear relationship. Signup and view all the answers

Define parallel lines.

Lines that never intersect and have the same slope. Signup and view all the answers

What is a parent function?

The simplest function in a family of functions. Signup and view all the answers

What are perpendicular lines?

Lines that intersect at a right angle. Signup and view all the answers

What is point-slope form?

An equation of a line defined by a point and its slope. Signup and view all the answers

Define range.

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

What is reflection in geometry?

The flipping of a figure over a line, creating a mirror image. Signup and view all the answers

Define relation in mathematics.

A set of ordered pairs. Signup and view all the answers

What is a scatter plot?

A graph that displays points representing values for two variables. Signup and view all the answers

Define slope.

The ratio of the change in y-coordinates to the change in x-coordinates. Signup and view all the answers

What is slope-intercept form?

The form of a linear equation expressed as y = mx + b. Signup and view all the answers

What is the standard form of a linear equation?

An equation written as Ax + By = C. Signup and view all the answers

What is a test point?

A specific point used to determine if a region of the graph is a solution to an inequality. Signup and view all the answers

What is a transformation in mathematics?

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

What is a translation?

A transformation that shifts a figure in a given direction. Signup and view all the answers

What is a vertex in the context of functions?

The highest or lowest point of a parabola. Signup and view all the answers

What is vertical compression?

A transformation that reduces the height of a graph. Signup and view all the answers

What is vertical stretch?

A transformation that increases the height of a graph. Signup and view all the answers

What does the vertical line test determine?

If a graph represents a function. Signup and view all the answers

What is an x-intercept?

The point where a graph intersects the x-axis. Signup and view all the answers

What is a y-intercept?

The point where a graph intersects the y-axis. Signup and view all the answers

What is a linear equation representative of direct variation?

y = kx, where k is a constant and k ≠ 0. Signup and view all the answers

What is the definition of a relation?

A set of ordered pairs, usually represented as (x, y). Signup and view all the answers

Study Notes

Functions and Relations

Absolute value function has the form f(x) = |mx + b| + c, where m ≠ 0.
A relation is a set of ordered pairs defining a relationship between x and y values.
The domain consists of all x-coordinates, while the range includes all y-coordinates.
A function occurs when each x-coordinate pairs with exactly one y-coordinate.

Graphs and Lines

The axis of symmetry divides a figure into two mirror-image parts.
A boundary of a graph in a linear inequality is a line in the coordinate plane, distinguishing solutions from nonsolutions.
The line of best fit represents the trend of data in scatter plots, minimizing the distance from points to the line.
Linear equations can be expressed in slope-intercept form y = mx + b, with m being the slope and b the y-intercept.

Variations and Correlations

Direct variation is modeled as y = kx where k is the constant of variation and cannot be zero.
Correlation assesses the strength of a relationship between two data sets, ranging from -1 to 1.
The correlation coefficient (r) quantifies the degree of correlation; values near 1 or -1 suggest strong linear relationships.

Slope and Intercepts

Slope quantifies how much y changes with a change in x, calculated as the ratio of change in y to change in x.
The x-intercept is where the graph crosses the x-axis, while the y-intercept is where it crosses the y-axis.

Linear Inequalities and Graphing

A linear inequality creates a half-plane on one side of the boundary line, indicating a region of solutions.
Perpendicular lines have slopes that are negative reciprocals, while parallel lines share the same slope.

Transformations and Properties

Transformations such as translations shift a graph's position without altering its shape.
The vertical-line test determines if a relation is a function; if any vertical line intersects the graph at more than one point, it is not a function.

Additional Concepts

The independent variable is the input of a function, while the dependent variable is the output.
The function rule describes the relationship between input and output variables.
The vertex of an absolute value function is the point where the direction of the graph changes.

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Description

Test your knowledge with these flashcards covering key concepts from Algebra 2 Unit 2. This set includes definitions and explanations for important terms such as absolute value functions and the axis of symmetry. Perfect for review and preparation for exams!