Warm up 1.a. Write the explicit formula for the following sequence -2, 3, 8, 13,… b. Find a40 2.a. Write the recursive formula for the following sequence 2, 8, 14, 20, … b. Find the next three terms.

Characteristics of Functions

Intercepts x-intercept – the point at which the line intersects the x-axis at (x, 0) y-intercept – the point at which the line intersects the y-axis at (0, y)

Find the x and y intercepts, then graph. -3x + 2y = 12

Find the x and y intercepts, then graph. 4x - 5y = 20

Increasing, Decreasing, or Constant Sweep from left to right and notice what happens to the y-values Finger Test- as you move your finger from left to right is it going up or down? Increasing goes up (L to R) Decreasing falls down (L to R) Constant is a horizontal graph

Continuous vs Discrete Continuous has NO breaks Discrete has gaps or breaks

Domain & Range D Domain  I Inputs X X-coordinates R Range O Outputs Y Y-values The domain of a relation is the set of all inputs or x-coordinates.    The range of a relation is the set of all the outputs or y-coordinates.

Notation Set Notation If the graph is discrete, list all of the inputs or outputs inside the squiggly brackets. Example: D= {1,2,4,5,7}

Notation Algebraic Notation Use equality and inequality symbols and variables to describe the domain and range. Examples: y > 5

Notation Interval Notation For each continuous section of the graph, write the starting and ending point separated by a comma. Parenthesis: point is not included in Domain/ Range Brackets: point is included in Domain/ Range Start End

Characteristics Domain: Range: Intercepts: Increasing or Decreasing?

Domain: Range: Intercepts: Increasing or Decreasing?

Just for practice, let’s look at an example that is NOT a linear function Domain: Range: Intercepts: