Algebra 1 EOC Review (2022) Flashcards
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Questions and Answers

What defines a function?

  • x-values can repeat
  • It has only one output for multiple inputs
  • It can fail the vertical line test
  • x-values do not repeat and it passes the vertical line test (correct)

    • What is the domain?

    Set of all of the possible x-values.

    What is the range?

    Set of all the possible y-values.

    What is a variable?

    <p>Not a number, a letter or symbol that stands for a number.</p> Signup and view all the answers

    Define independent variable.

    <p>The input or cause in a situation or problem.</p> Signup and view all the answers

    Define dependent variable.

    <p>The output or result in a situation or problem.</p> Signup and view all the answers

    What are other names for 'x'?

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

    What are other names for 'y'?

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

    What is a discrete function?

    <p>Data appears as individual points on a graph.</p> Signup and view all the answers

    What is a continuous function?

    <p>Data appears as a smooth curve on a graph.</p> Signup and view all the answers

    What does 'm' stand for in the equation y = mx + b?

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

    What does 'b' stand for in the equation y = mx + b?

    <p>The y-intercept</p> Signup and view all the answers

    What is the definition of slope?

    <p>The steepness of a line.</p> Signup and view all the answers

    What slope does a horizontal line have?

    <p>Slope = 0</p> Signup and view all the answers

    What slope does a vertical line have?

    <p>Undefined slope</p> Signup and view all the answers

    What is the x-intercept?

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

    What is the y-intercept?

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

    What is a linear inequality?

    <p>An equation with a &lt; or =, &gt; or = in place of the =</p> Signup and view all the answers

    How do the slopes of parallel lines compare?

    <p>They are the same.</p> Signup and view all the answers

    How do the slopes of perpendicular lines compare?

    <p>They are opposite reciprocals.</p> Signup and view all the answers

    What is a line of best fit?

    <p>A line drawn through the points on a scatterplot.</p> Signup and view all the answers

    What is the solution of a system of equations?

    <p>Where the lines touch or cross.</p> Signup and view all the answers

    Where are the solutions of a quadratic function?

    <p>At the x-intercepts.</p> Signup and view all the answers

    What are 'like terms'?

    <p>Mathematical terms that have the same variables raised to the same exponents.</p> Signup and view all the answers

    How do you combine like terms?

    <p>Add their coefficients.</p> Signup and view all the answers

    How do you multiply exponents of like variables?

    <p>Add them.</p> Signup and view all the answers

    How do you divide exponents of like variables?

    <p>Subtract them.</p> Signup and view all the answers

    What is the rate of change on a graph?

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

    What is an integer?

    <p>A whole number, both positive and negative numbers.</p> Signup and view all the answers

    What is the Quadratic Formula?

    <p>x = -b ± √(b² - 4ac)/2a</p> Signup and view all the answers

    What is the maximum or minimum of a quadratic function?

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

    When do you flip an inequality symbol?

    <p>Anytime you multiply or divide by a negative number.</p> Signup and view all the answers

    What is the Substitution Method?

    <p>Solving one equation for one variable and plugging it into another.</p> Signup and view all the answers

    What is the Elimination Method?

    <p>Manipulation is needed in order for x-values or y-values to cancel each other out.</p> Signup and view all the answers

    What is the solution to a system of linear inequalities?

    <p>The intersection of the two half-planes.</p> Signup and view all the answers

    What is y= and f(x)=?

    <p>These are the same.</p> Signup and view all the answers

    How do you solve when written in function notation?

    <p>Replace x with (-2) and solve.</p> Signup and view all the answers

    What are Geometric Sequences?

    <p>A pattern in which you multiply or divide by a common number.</p> Signup and view all the answers

    What is the Axis of Symmetry?

    <p>The equation x=0 is the axis of symmetry for a parabola in standard form.</p> Signup and view all the answers

    What are Linear functions?

    <p>A function that has only one answer for y for every x.</p> Signup and view all the answers

    What are Exponential functions?

    <p>Functions where the variable is the exponent.</p> Signup and view all the answers

    What is an Arithmetic Sequence?

    <p>A pattern in which you add a number each time.</p> Signup and view all the answers

    What is a positive correlation?

    <p>A relationship where one variable increases as the other also increases.</p> Signup and view all the answers

    What is a negative correlation?

    <p>A relationship where one variable increases and the other decreases.</p> Signup and view all the answers

    What is the Correlation Coefficient?

    <p>A number between -1 and 1 that indicates strength and direction of correlation.</p> Signup and view all the answers

    What is Causation?

    <p>The reason something occurs.</p> Signup and view all the answers

    What is the Distributive Property?

    <p>Multiply a number or variable to everyone inside parentheses.</p> Signup and view all the answers

    What are Perfect Squares?

    <p>1, 4, 9, 16, 25, etc.</p> Signup and view all the answers

    What is the Slope-intercept form?

    <p>y = mx + b</p> Signup and view all the answers

    What is the Point-Slope Form?

    <p>(y - y*) = m (x - x*)</p> Signup and view all the answers

    What is the Standard Form of a line?

    <p>Ax + By = C</p> Signup and view all the answers

    What is a Binomial?

    <p>A polynomial with two terms.</p> Signup and view all the answers

    What is a Parabola?

    <p>The shape of the graph of a quadratic function.</p> Signup and view all the answers

    What is the Vertex of a parabola?

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

    What is the maximum and minimum value in a quadratic?

    <p>The highest or lowest output of a quadratic function.</p> Signup and view all the answers

    What is quadratic regression?

    <p>y1 ~ ax1^2 + bx1 + c</p> Signup and view all the answers

    What is a Factor?

    <p>A binomial that is multiplied by another binomial to find a product.</p> Signup and view all the answers

    What does a Solid line indicate in inequalities?

    <p>≤ or ≥, can be a solution if on the line.</p> Signup and view all the answers

    What does a Dashed line indicate in inequalities?

    <p>&lt; or &gt;, can't be a solution if on the line.</p> Signup and view all the answers

    Study Notes

    Functions and Variables

    • A function has unique x-values that pass the vertical line test.
    • Domain refers to all possible x-values of a function.
    • Range includes all possible y-values.
    • A variable is represented by a letter or symbol and does not equal a number.
    • The independent variable is the controlled input (x-variable).
    • The dependent variable is the outcome that cannot be controlled (y-variable).

    Graphing and Types of Functions

    • Discrete functions display data as individual points, indicating non-divisible data.
    • Continuous functions show data as a smooth curve, representing divisible data.
    • The graph of a linear function shows a straight line; quadratic functions form parabolic curves.

    Equations and Slopes

    • In the slope-intercept form (y = mx + b), (m) signifies the slope and (b) the y-intercept.
    • Changing (m) alters the steepness of a line.
    • Changing (b) shifts the line up or down.
    • Slope is calculated as the vertical change divided by the horizontal change.

    Intercepts

    • The x-intercept is where a graph crosses the x-axis (coordinates ( (x, 0) )).
    • The y-intercept is where it crosses the y-axis (coordinates ( (0, y) )).

    Inequalities and Systems

    • A linear inequality contains inequality symbols (<, >) instead of an equals sign.
    • Parallel lines have equal slopes, while perpendicular lines have slopes that are opposite reciprocals.

    Correlation

    • Positive correlation indicates that as one variable increases, the other does as well.
    • Negative correlation shows that as one variable increases, the other decreases.
    • The correlation coefficient ranges from -1 to 1, reflecting the strength and direction of a relationship.

    Sequences and Functions

    • Geometric sequences involve multiplying or dividing by a common number.
    • Arithmetic sequences involve adding a constant number each time.
    • Exponential functions grow or decay at a constant factor over equal intervals.

    Quadratics

    • The quadratic formula is used to find solutions for quadratic equations: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}).
    • A parabola has a vertex, which indicates the maximum or minimum value.

    Systems of Equations

    • A system of equations contains multiple equations with the same variables.
    • Solutions occur at points where the lines intersect in a system.
    • Substitution and elimination methods are used to solve systems of equations.

    Properties and Transformations

    • The Distributive Property applies when multiplying a number across terms in parentheses.
    • Transformations like vertical and horizontal translations involve shifting a graph without changing its shape.

    Regression and Best Fit

    • Linear regression helps find the equation of the best fit line through scatterplot data.
    • Exponential regression identifies equations for exponential growth or decay.

    Special Types of Lines

    • A solid line indicates a solution can exist on the line (≥ or ≤).
    • A dashed line indicates no solutions exist on the line (< or >).

    Additional Concepts

    • Positive or negative c correlations reflect a consistent relationship trend.
    • An asymptote is a line that a graph approaches but never crosses.

    Final Thoughts

    • Understanding functions, their graphs, slopes, and intercepts is crucial in algebra.
    • Knowing how to identify and manipulate equations will aid significantly in solving algebra problems.

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    Description

    These flashcards provide a comprehensive review of key algebraic concepts essential for the Algebra 1 End-of-Course exam. Each card features important definitions such as function, domain, range, and variable, helping students reinforce their understanding. Perfect for quick study sessions and exam preparation.

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