Algebra 1 - Chapter 3 Vocabulary

discrete

A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values. A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers.: Graph the continuous function: y = x2 for all Reals.

dependent variable

A dependent variable is a variable whose value depends upon independent variable s. The dependent variable is what is being measured in an experiment or evaluated in a mathematical equation. The dependent variable is sometimes called "the outcome variable." In a simple mathematical equation, for example: a = b/c.

horizontal shrink

A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x).

linear function

A linear function is any function that graphs to a straight line. What this means mathematically is that the function has either one or two variables with no exponents or powers. If the function has more variables, the variables must be constants or known variables for the function to remain a linear function.

parent function

A parent function is the simplest function of a family of functions. For the family of quadratic functions, y = ax2 + bx + c, the simplest function. of this form is y = x2. The "Parent" Graph: The simplest parabola is y = x2, whose graph is shown at the right.

reflection

A transformation in which a geometric figure is reflected across a line, creating a mirror image. That line is called the axis of reflection.

transformation

A transformation is a general term for four specific ways to manipulate the shape of a point, a line, or shape. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation. Types of transformations in math. Translation. Reflection.

vertical stretch

A vertical compression is the squeezing of the graph towards the x-axis. If the original (parent) function is y = f (x), the vertical stretching or compressing of the function is the function a f(x). if 0 < a < 1 (a fraction), the graph is compressed vertically by a factor. of a units.

horizontal stretch

A vertical stretching is the stretching of the graph away from the x-axis. A vertical compression is the squeezing of the graph towards the x-axis. If the original (parent) function is y = f (x), the vertical stretching or compressing of the function is the function a f(x).

vertical shrink

Based on the definition of vertical shrink, the graph of y1(x) should look like the graph of f (x), vertically shrunk by a factor of 1/2. Take a look at the graphs of f (x) and y1(x). Notice that the x-intercepts have not moved. Function (2), g (x), is a sine function.

slope

Definition & Formulas. The slope is a measure of the steepness of a line, or a section of a line, connecting two points. In this lesson, you will use several different formulas for slope and learn how those formulas relate to the steepness of a line. Supplemental Math: Study Aid / Math Courses.

linear equation in two variables

Each linear equation in two variables defined a straight line. To solve a system of two linear equations in two variables, we graph both equations in the same coordinate system. The coordinates of any points that graphs have in common are solutions to the system, since they satisfy both equations.

vertex

From Latin: vertex "highest point" Definition: The common endpoint of two or more rays or line segments. Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices.

function notation

Function notation is a method of writing algebraic variables as functions of other variables. Most often, functions are portrayed as a set of x/y coordinates, with the vertical y-axis serving as a function of x. For example, writing "f(x) = 3x" is the same as writing "y = 3x."

x-intercept

Function notation is a method of writing algebraic variables as functions of other variables. Most often, functions are portrayed as a set of x/y coordinates, with the vertical y-axis serving as a function of x. For example, writing "f(x) = 3x" is the same as writing "y = 3x."

nonlinear function

Graphically, a linear function is a function whose graph is a line. Algebraically, a linear function can be defined as a polynomial with highest exponent equal to 1 or a horizontal line (y = c where c is a constant).

constant function

In mathematics, a constant function is a function whose (output) value is the same for every input value. For example, the function y ( x ) = 4 {\displaystyle y(x)=4} is a constant function because the value of y ( x ) {\displaystyle y(x)} is 4 regardless of the input value (see image).

continuous

In mathematics, a continuous function is, roughly speaking, a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function. A continuous function with a continuous inverse function is called a homeomorphism.

family of functions

In mathematics, a parent function is the simplest function of a family of functions that preserves the definition (or shape) of the entire family. ... This is therefore the parent function of the family of quadratic equations.

independent variable

Independent variable definition. An independent variable is a variable that represents a quantity that is being manipulated in an experiment. A dependent variable represents a quantity whose value depends on those manipulations.

Rise/Run (rise over run)

Rise/Run (Rise divided by Run) gives us the slope of the line. See: Slope. Equation of a Straight Line.

absolute value function

The Absolute Value Function, and its Properties. One of the most used functions in mathematics is the absolute value function. ... Absolute Value Function The absolute value of a real number x, |x|, is. |x| = { x.

range

The difference between the lowest and highest values. In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6. Range can also mean all the output values of a function. See: Range of a function. The Range (Statistics)

domain

The set of values of the independent variable(s) for which a function or relation is defined. Typically, this is the set of x-values that give rise to real y-values. Note: Usually domain means domain of definition, but sometimes domain refers to a restricted domain.

slope- intercept form

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form.

vertex form

The vertex form of a quadratic function is given by. f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. FYI: Different textbooks have different interpretations of the reference "standard form" of a quadratic function.

translation

Translation Definition. Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized. In a translation, every point of the object must be moved in the same direction and for the same distance.

y-intercept

in the Context of Word Problems. In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept, where the line crosses the y-axis.