Questions and Answers
What is a recursive function?
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?
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What is the vertex of a quadratic function?
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The product of a rational number and an irrational number is always irrational.
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The sum of two irrational numbers is always irrational.
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The product of two irrational numbers can be either real or irrational.
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The sum of a rational number and an irrational number is always rational.
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What is an arithmetic sequence?
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What is a geometric sequence?
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What is the formula for a geometric sequence?
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What is the Distance Formula?
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What is the midpoint formula?
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What are inverse functions?
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What defines a piecewise function?
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What is compound interest?
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What is the Compound Interest Formula?
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What is exponential growth?
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What is the absolute value function?
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What is the Discriminant?
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What does a positive discriminant indicate?
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What does a negative discriminant indicate?
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What does a zero discriminant indicate?
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What is the average rate of change formula?
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An even function is symmetrical with respect to the y-axis.
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An odd function is symmetrical with respect to the origin.
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What is an inverse function?
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What is standard deviation?
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What is linear regression?
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What is a linear regression equation?
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How is the domain represented on a graph?
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How is the range represented on a graph?
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What is the slope-intercept form of a linear equation?
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What is the standard form of a linear equation?
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What is a quadratic function?
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What is the Exponential Function Equation?
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A positive value of 'a' in a quadratic function results in a parabola that opens down.
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A negative value of 'a' in a quadratic function results in a parabola that opens up.
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What is the axis of symmetry for a quadratic function?
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What transformation does a negative 'a' value apply?
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What does the 'h' value in transformations indicate?
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What does the 'k' value in transformations indicate?
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What is the parent function of a quadratic?
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Irrational numbers can be expressed as a ratio of two integers.
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What are imaginary numbers?
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What is the mean absolute deviation?
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What is variance?
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What is a normal distribution curve?
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What are matrices?
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What is scalar multiplication?
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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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