Algebra 2 Unit 2 Flashcards
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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?

    <p>The ratio of two variables in direct variation.</p> Signup and view all the answers

    What does correlation indicate?

    <p>The strength of the relationship between two data sets.</p> Signup and view all the answers

    What is the correlation coefficient?

    <p>It indicates the strength of the correlation.</p> Signup and view all the answers

    What does the dependent variable represent?

    <p>It represents the output or result in a function.</p> Signup and view all the answers

    What is direct variation?

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

    Define domain.

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

    What is function notation?

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

    What does the function rule determine?

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

    What is a half-plane?

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

    Define independent variable.

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

    What is a line of best fit?

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

    What is a linear equation?

    <p>An equation whose graph forms a straight line.</p> Signup and view all the answers

    What is a linear function?

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

    What is a linear inequality?

    <p>An inequality that represents a linear relationship.</p> Signup and view all the answers

    Define parallel lines.

    <p>Lines that never intersect and have the same slope.</p> Signup and view all the answers

    What is a parent function?

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

    What are perpendicular lines?

    <p>Lines that intersect at a right angle.</p> Signup and view all the answers

    What is point-slope form?

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

    Define range.

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

    What is reflection in geometry?

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

    Define relation in mathematics.

    <p>A set of ordered pairs.</p> Signup and view all the answers

    What is a scatter plot?

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

    Define slope.

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

    What is slope-intercept form?

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

    What is the standard form of a linear equation?

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

    What is a test point?

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

    What is a transformation in mathematics?

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

    What is a translation?

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

    What is a vertex in the context of functions?

    <p>The highest or lowest point of a parabola.</p> Signup and view all the answers

    What is vertical compression?

    <p>A transformation that reduces the height of a graph.</p> Signup and view all the answers

    What is vertical stretch?

    <p>A transformation that increases the height of a graph.</p> Signup and view all the answers

    What does the vertical line test determine?

    <p>If a graph represents a function.</p> Signup and view all the answers

    What is an x-intercept?

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

    What is a y-intercept?

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

    What is a linear equation representative of direct variation?

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

    What is the definition of a relation?

    <p>A set of ordered pairs, usually represented as (x, y).</p> 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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    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!

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