Algebra II w/ trig

 Coordinate Plane

 Ordered pair: (x, y)  Relation: a set of ordered pairs(mapping, ordered pairs, table, or graphing)  Domain: x-values (input values)  Range: y-values (output values)

 Function: a relation in which each element of the domain is paired with exactly one element of the range. ***every function is a relation, but not every relation is a function***  Vertical Line Test: if the vertical line intersects a given graph at no more than one point, then the graph represents a function  Function Notation: the correspondence between values of the domain, x, and values of the range, y; where y = f(x) x value is called the independent variable y value is called the dependent variable

I. Identify the domain and the range. Then tell if the relation is a function. A. InputOutput

B. C.

D.E.

II. Find each value if and g(x) = -2x + 3. A. B. C.

D.E.

2.2 Linear Equations Linear Equations: Has no operations other than addition, subtraction, and multiplication of a variable by a constant. The variables may not be multiplied together or appear in the denominator. A linear equation does contain variables with exponents other than 1. The graph of a linear equation is a line. Examples: Linear EquationsNot a linear equations 5x -3y = 7 x + xy = 1 x = 9 y = 1/x 6x = -3t-15

I. Decide if the function is linear. Explain A. 6y – 7 = x B. 9x = 18/y C. f(x) = 2 – x/11 D. h(x) = √x + 3 E. f(x) = 4x 2

 Standard form of Linear Equations: Ax + By = C  To graph a linear equation, you only need two points: x-intercept: where it crosses the x-axis (x, 0) y-intercept: where it crosses the y-axis (0, y) To find x-intercept: set y = 0, solve for x To find y-intercept: set x = 0, solve for y

II. Write each equation in standard form. Identify A, B, and C. A. 2x = 4y -1B.

III. Find the x-intercept and y-intercept of the graph of each equation and then graph the equation. A. 2x + 7y = 14B. y = 3x – 6

C. y = 3D. x = -2