Common Core Math 8 Standards:

8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output (function notation is not required in Grade 8).

8.F.A.2* Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.A.3* Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A= s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1, 1), (2, 4) and (3, 9), which are not on a straight line. (SC 8)

8.F.B.4* Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

8.EE.B.5* Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.B.6* Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin, and the equation y = mx + b for a line intercepting the vertical axis at b.

Unit Vocabulary

Coefficient: The number that is multiplied by the variable in an algebraic expression.

Constant: A value that does not change.

Coordinate Plane: A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis

Decreasing: A function with a graph that moves downward as it is followed from left to right.

Dependent: The output of a function; a variable whose value depends on the value of the input, or independent variable.

Domain: The set of all possible input values of a function.

*Functions: An input-output relationship that has exactly one output for each input.

*Function Tables: A table of ordered pairs that represent solutions of a function.

Horizontal: Parallel to the x-axis; a line with a zero slope

Increasing: A function with a graph that moves upward as it is followed from left to right

Independent: The input of a function; a variable whose value determines the value of the output, or dependent variable.

Initial Value: The starting value of a function, when x=0

Input: The value substituted into an expression or function.

Integer: The set of whole numbers and their opposites

Linear: As the input increases, the output increases at a constant rate

*Linear Function: A function whose graph is a straight line.

*Mapping: Pairing each member of the domain with each member of the range.

*Nonlinear: A relationship between two variables in which the data do not increase or decrease together at the same rate.

Order of Operations: A rule for evaluating expressions: First perform the operations in parentheses, then compute powers and roots, then perform all multiplication and division from left to right, and then perform all addition and subtraction from left to right.

Ordered Pairs: A pair of numbers that can be used to locate a point on a coordinate plane.

Origin: The point where the x-axis and y-axis intersect on the coordinate plane; (0, 0).

Output: The value that results from the substitution of a given input into an expression or function.

Parallel Lines: Lines in a plane that do not intersect.

proportional relationships: A relationship between two quantities in which the ratio of one quantity to the other quantity is constant.

Range: The set of all possible output values of a function.

Rate of Change: A ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

Rule: A method for describing the relationship between two variables.

Steepness: How slanted a line is; how close to horizontal or vertical

*Slope (+, -, no, undefined): A measure of the steepness of a line on a graph; the rise divided by the run.

unit rate: A rate in which the second quantity in the comparison is one unit.

Vertical: Parallel to the y-axis; undefined slope

Vertical Lines: lines with an undefined slope

*Vertical Line Test: A test used to determine whether a relation is a function. If any vertical line crosses the graph of a relation more than once, the relation is not a function.

X-axis: The horizontal axis on a coordinate plane.

X-coordinate: The first number in an ordered pair; it tells the distance to move right or left from the origin (0, 0).

X-intercept: The x-coordinate of the point where the graph of a line crosses the x-axis.

Y-axis: The vertical axis on a coordinate plane.

Y-coordinate: The second number in an ordered pair; it tells the distance to move up or down from the origin (0, 0).

Y-intercept: The y-coordinate of the point where the graph of a line crosses the y-axis.