Praxis 5162 Algebra Flashcards
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Questions and Answers

What is a recursive function?

  • A function that does not depend on previous terms.
  • A function that can only be used once.
  • A function that goes step by step. (correct)
  • A function with only one output.

    • What defines an explicit function?

    A function in which the dependent variable can be expressed directly in terms of the independent variable.

    What is a composite function?

    A combination of two functions where the output of the first function becomes the input for the second function.

    What is the vertex form of a quadratic function?

    <p>y = a(x - h)² + k</p> Signup and view all the answers

    What is the vertex of a quadratic function?

    <p>(h, k)</p> Signup and view all the answers

    The product of a rational number and an irrational number is always irrational.

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

    The sum of two irrational numbers is always irrational.

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

    The product of two irrational numbers can be either real or irrational.

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

    The sum of a rational number and an irrational number is always rational.

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

    What is an arithmetic sequence?

    <p>A sequence where each term is found by adding the same number to the previous term.</p> Signup and view all the answers

    What is a geometric sequence?

    <p>A sequence where each term is found by multiplying the previous term by the same number.</p> Signup and view all the answers

    What is the formula for a geometric sequence?

    <p>A(n) = a1 * r^(n - 1)</p> Signup and view all the answers

    What is the Distance Formula?

    <p>d = √[(x₂ - x₁)² + (y₂ - y₁)²]</p> Signup and view all the answers

    What is the midpoint formula?

    <p>((x₁ + x₂)/2, (y₁ + y₂)/2)</p> Signup and view all the answers

    What are inverse functions?

    <p>Functions that switch x and y and solve for y.</p> Signup and view all the answers

    What defines a piecewise function?

    <p>A function composed of two or more functions.</p> Signup and view all the answers

    What is compound interest?

    <p>Interest earned on both the principal amount and any interest already earned.</p> Signup and view all the answers

    What is the Compound Interest Formula?

    <p>A = P(1 + r/n)^(nt)</p> Signup and view all the answers

    What is exponential growth?

    <p>A growth pattern where individuals reproduce at a constant rate.</p> Signup and view all the answers

    What is the absolute value function?

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

    What is the Discriminant?

    <p>b² - 4ac</p> Signup and view all the answers

    What does a positive discriminant indicate?

    <p>2 real solutions</p> Signup and view all the answers

    What does a negative discriminant indicate?

    <p>No real solutions</p> Signup and view all the answers

    What does a zero discriminant indicate?

    <p>1 real solution</p> Signup and view all the answers

    What is the average rate of change formula?

    <p>(y2 - y1) / (x2 - x1)</p> Signup and view all the answers

    An even function is symmetrical with respect to the y-axis.

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

    An odd function is symmetrical with respect to the origin.

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

    What is an inverse function?

    <p>A function in which two variables are inversely proportional.</p> Signup and view all the answers

    What is standard deviation?

    <p>A measure of variability that describes the average distance of every score from the mean.</p> Signup and view all the answers

    What is linear regression?

    <p>A method of finding the best model for a linear relationship between explanatory and response variables.</p> Signup and view all the answers

    What is a linear regression equation?

    <p>The equation for the line of best fit.</p> Signup and view all the answers

    How is the domain represented on a graph?

    <p>How far left to how far right, all x values.</p> Signup and view all the answers

    How is the range represented on a graph?

    <p>How far down to how far up, all y values.</p> Signup and view all the answers

    What is the slope-intercept form of a linear equation?

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

    What is the standard form of a linear equation?

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

    What is a quadratic function?

    <p>A function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.</p> Signup and view all the answers

    What is the Exponential Function Equation?

    <p>y = ab^x</p> Signup and view all the answers

    A positive value of 'a' in a quadratic function results in a parabola that opens down.

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

    A negative value of 'a' in a quadratic function results in a parabola that opens up.

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

    What is the axis of symmetry for a quadratic function?

    <p>x = -b / (2a)</p> Signup and view all the answers

    What transformation does a negative 'a' value apply?

    <p>Flips the parabola.</p> Signup and view all the answers

    What does the 'h' value in transformations indicate?

    <p>Left/right movement.</p> Signup and view all the answers

    What does the 'k' value in transformations indicate?

    <p>Up/down movement.</p> Signup and view all the answers

    What is the parent function of a quadratic?

    <p>y = x²</p> Signup and view all the answers

    Irrational numbers can be expressed as a ratio of two integers.

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

    What are imaginary numbers?

    <p>Square roots of negative numbers.</p> Signup and view all the answers

    What is the mean absolute deviation?

    <p>The average distance between each data value and the mean.</p> Signup and view all the answers

    What is variance?

    <p>Standard deviation squared.</p> Signup and view all the answers

    What is a normal distribution curve?

    <p>The bell-shaped curve that results from plotting continuous variation data.</p> Signup and view all the answers

    What are matrices?

    <p>An arrangement of numbers in rows and columns.</p> Signup and view all the answers

    What is scalar multiplication?

    <p>The process of multiplying each element of a matrix by a real number.</p> Signup and view all the answers

    Study Notes

    Functions and Sequences

    • Recursive Function: A function that calculates successive values step by step starting from an initial condition.
    • Explicit Function: A function that defines the dependent variable directly in terms of the independent variable.
    • Composite Function: A function formed by applying one function to the results of another, where the output from the first serves as the input for the second.
    • Piecewise Function: A function consisting of multiple sub-functions, each applicable to a specific interval of the domain.
    • Inverse Function: Achieved by switching the dependent and independent variables and solving for the new dependent variable.

    Quadratic Functions

    • Vertex Form: Represents a quadratic function as ( y = a(x-h)^2 + k ), where (h, k) is the vertex.
    • Vertex: Key point of a quadratic function represented as (h, k).
    • Axis of Symmetry: A vertical line given by ( x = -\frac{b}{2a} ) that bisects the parabola.

    Sequence Types

    • Arithmetic Sequence: Each term is generated by adding a constant to the previous term.
    • Geometric Sequence: Each term is created by multiplying the previous term by a constant ratio.
    • Geometric Sequence Formula: Defined as ( A(n) = a_1 r^{n-1} ).

    Formulas and Calculations

    • Distance Formula: Used to calculate the distance between two points: ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ).
    • Midpoint Formula: Provides the midpoint of a line segment as ( \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) ).
    • Compound Interest Formula: Given by ( A = P(1+\frac{r}{n})^{nt} ) for calculating compound interest over time.

    Discriminants

    • Discriminant: Calculated as ( b^2 - 4ac ) to determine the nature of the roots of a quadratic equation.
    • Positive Discriminant: Indicates two real solutions.
    • Negative Discriminant: Suggests no real solutions exist.
    • Zero Discriminant: Indicates exactly one real solution.

    Function Types

    • Even Function: Exhibits symmetry about the y-axis, characterized by ( f(x) = f(-x) ).
    • Odd Function: Exhibits symmetry about the origin, shown by ( f(-x) = -f(x) ).

    Statistical Concepts

    • Standard Deviation: Measures variability, quantifying average distances of scores from the mean.
    • Variance: Defined as the square of the standard deviation.
    • Mean Absolute Deviation: The average of the distances between each data point and the mean.

    Graphical Analysis

    • Domain: Represents the set of all possible x-values of a function.
    • Range: Represents the set of all possible y-values of a function.
    • Slope-Intercept Form: Written as ( y = mx + b ), where m is the slope and b is the y-intercept.
    • Standard Form: Represented as ( Ax + By = C ).

    Miscellaneous Concepts

    • Exponential Growth: Describes populations reproducing at a constant rate.
    • Absolute Value Function: Defined as ( f(x) = |x| ), reflecting distances from zero.
    • Imaginary Numbers: Result from the square root of negative numbers.
    • Normal Distribution Curve: A bell-shaped curve illustrating the distribution of continuous data.
    • Matrices: Organized arrays of numbers used in various calculations, such as linear transformations.
    • Scalar Multiplication: Involves multiplying each element in a matrix by a scalar value.

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    Test your understanding of key algebra concepts with these flashcards from Praxis 5162. Each card features critical definitions related to functions, including recursive, explicit, and composite functions. Perfect for quick reviews or studying for exams.

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