Unit+2

=Unit 2 Function, Equations and Graphs=

Vocabulary

 * absolute value function (p. 86) || linear function (p. 62) || slope-intercept form (p. 65) ||
 * constant of variation (p. 72) || linear inequality (p. 99) || standard form (p. 63) ||
 * dependent variable (p. 62) || mapping diagram (p. 56) || translation (p. 91) ||
 * direct variation (p. 72) || parent function (p. 91) || trend line (p. 80) ||
 * domain (p. 56) || point-slope form (p. 65) || vertical-line test (p. 57) ||
 * function (p. 57) || range (p. 56) || //x//-intercept (p. 63) ||
 * function notation (p. 58) || relation (p. 55) || //y//-intercept (p. 63) ||
 * independent variable (p. 62) || scatter plot (p. 80) ||  ||
 * linear equation (p. 62) || slope (p. 64) ||

2-1 Objectives
A **relation** is a set of ordered pairs that can be represented by points in the coordinate plane or by a **mapping diagram.** The **domain** of a relation is the set of //x//-coordinates. The **range** is the set of //y//-coordinates. When each element of the domain of a relation is paired with exactly one element of the range, the relation is a **function.** You can write a function using the notation //f//(//x//), called **function notation.**
 * 1) To graph relations (p. 55)
 * 2) To identify functions (p. 57

2-2 Objectives
The graph of a **linear function** is a line. You can represent a linear function with a **linear equation.** In a function, the value of //y// depends on the value of //x//, so //y// is the **dependent variable** and //x// is the **independent variable.** Given two points on a line, the **slope** of the line is the ratio of the difference of the //y//-coordinates to the corresponding difference of the //x//-coordinates. The slope equals the coefficient of //x// when you write a linear equation in **slope-intercept form.** You can also write a linear equation in **point-slope form** or **standard form.** You can use the slopes of lines to determine whether or not they are parallel, perpendicular, or horizontal. A vertical line has no slope.
 * 1) To graph linear equations (p. 62)
 * 2) To write equations of lines (p. 64)

2-3 Objectives
A linear equation of the form //y// = //kx// represents a **direct variation.** The **constant of variation** is //k//. You can use proportions to solve some direct variation problems.
 * 1) To write and interpret direct variation equations (p. 72)

2-4 Objectives
You can use mathematical models such as **scatter plots** to show relationships between data sets. You can use the models to make predictions about the data set. Sometimes you can draw a **trend line** to model the relation and make predictions.
 * 1) To write linear equations that model real-world data (p. 78)
 * 2) To make predictions from linear models (p. 79)

2-5 and 2-6 Objectives
The **absolute value function** //y// = | //x// | has a graph in the shape of a V. It is the **parent function** for the family of functions of the form //y// = | //x// + //h// | + //k//. The maximum or minimum point of the V is the vertex of the graph. The value of //h// represents a horizontal translation of the parent graph by //h// units left (//h// is positive) or right (//h// is negative). The //k// represents a vertical translation of the graph by //k// units up (//k// is positive) or down (//k// is negative). A combination of a horizontal and a vertical translation is a diagonal translation.
 * 1) To graph absolute value functions (p. 86)
 * 2) To analyze vertical translations (p. 91)
 * 3) To analyze horizontal translations (p. 92)

2-7 Objectives
A **linear inequality** describes a region of the coordinate plane that has a boundary. To graph an inequality involving two variables, first graph the boundary. Then decide which side of the boundary contains solutions. Points on a dashed boundary are not solutions. Points on a solid boundary are solutions.
 * 1) To graph linear inequalities (p. 99)
 * 2) To graph absolute value inequalities (p. 101)