Question

Vocabulary words
Definition or Description


Lesson 2: Relations & Functions
domain




range


equation




function




graph




mapping diagram




ordered pair




relation




Vertical Line Test




Lesson 3: Relations & Functions Discussion
No new vocab this lesson
Lesson 4: Naming, Evaluating, & Interpreting Functions
dependent variable




independent variable


evaluating a function




function notation




Lesson 5: Representing Functions
input-output table




Lesson 6: Linear Functions from Situations
linear function




origin




quantities




scale




slope




slope-intercept form




y-intercept




Lesson 7: Piecewise Linear Functions from Situations
absolute value function




interval




piecewise function




piecewise linear function




restricted function




step-function




Lesson 8: Exponential Functions from Situations
depreciation




exponential function




Lesson 9: Quadratic Functions from Situations
axis of symmetry of a parabola




parabola




quadratic equation




quadratic formula




vertex of a parabola




x-intercepts of a parabola




y-intercept of a parabola

Answer 1

Here are concise definitions/descriptions for each vocabulary word in your list.

Lesson 2: Relations & Functions
- domain: The set of all allowable input values (usually x-values) for a relation or function.
- range: The set of all output values (usually y-values) produced by a relation or function.
- equation: A mathematical statement that two expressions are equal, often involving variables.
- function: A relation in which each input corresponds to exactly one output.
- graph: A visual representation of a relation or function, typically as points or a curve on a coordinate plane.
- mapping diagram: A diagram showing how each element of the domain is paired with an element of the range (using arrows).
- ordered pair: A pair (x, y) that gives the coordinates of a point in the plane; order matters.
- relation: Any set of ordered pairs; a pairing between inputs and outputs.
- Vertical Line Test: A test for determining whether a graph represents a function — if any vertical line intersects the graph more than once, the graph is not a function.

Lesson 3
- No new vocabulary.

Lesson 4: Naming, Evaluating, & Interpreting Functions
- dependent variable: The output variable whose value depends on the input (commonly y).
- independent variable: The input variable that can be chosen freely (commonly x).
- evaluating a function: Finding the output value by substituting a specific input into the function’s formula.
- function notation: A way to name functions, e.g., f(x) denotes the value of function f at input x.

Lesson 5: Representing Functions
- input-output table: A table listing input values and their corresponding output values for a function or relation.

Lesson 6: Linear Functions from Situations
- linear function: A function whose graph is a straight line; typically has form y = mx + b.
- origin: The point (0, 0) where the x- and y-axes intersect.
- quantities: Measurable amounts or variables in a real-world situation that can be represented mathematically.
- scale: The spacing or unit lengths used on axes that relate graph distances to actual quantities.
- slope: The rate of change of a line, calculated as rise/run = (y2 − y1)/(x2 − x1).
- slope-intercept form: The form y = mx + b for a line, where m is the slope and b is the y-intercept.
- y-intercept: The point where a graph crosses the y-axis; its coordinates are (0, b).

Lesson 7: Piecewise Linear Functions from Situations
- absolute value function: A function f(x) = |x| that outputs the nonnegative magnitude of x; its graph is a V-shape.
- interval: A contiguous set of real numbers between two endpoints (may be open or closed).
- piecewise function: A function defined by different formulas on different intervals of the domain.
- piecewise linear function: A piecewise function whose pieces are linear (straight-line segments).
- restricted function: A function whose domain has been limited to a specific subset of values.
- step-function: A function that is constant on intervals and jumps between values (e.g., floor function).

Lesson 8: Exponential Functions from Situations
- depreciation: A decrease in the value of an asset over time; often modeled by exponential decay.
- exponential function: A function in which a constant base is raised to a variable exponent, e.g., f(x) = a·b^x with b > 0 and b ≠ 1.

Lesson 9: Quadratic Functions from Situations
- axis of symmetry of a parabola: The vertical line that divides a parabola into mirror-image halves; for y = ax^2 + bx + c it is x = −b/(2a).
- parabola: The U-shaped graph of a quadratic function.
- quadratic equation: An equation of the form ax^2 + bx + c = 0 where a ≠ 0.
- quadratic formula: The formula x = [−b ± sqrt(b^2 − 4ac)] / (2a) that gives solutions to ax^2 + bx + c = 0.
- vertex of a parabola: The highest or lowest point of a parabola (turning point); for y = ax^2 + bx + c it occurs at x = −b/(2a).
- x-intercepts of a parabola: The points where the parabola crosses the x-axis; solutions to the quadratic equation.
- y-intercept of a parabola: The point where the parabola crosses the y-axis; for y = ax^2 + bx + c it is (0, c).

If you want, I can add brief examples or diagrams for any of these terms.