the graph below represents marias distance from home one day as she rode her bike to meet friends...

The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home.

1. What do the horizontal lines on the graph represent?2. Where in the graph shows her taking care of the 2

errands?

3. Compare how she traveled at the beginning to how she traveled at the very end.

4. Create Maria’s story so that it matches the graph.

Characteristics of Functions

Notation• Interval – represents an interval

as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included• Set – using inequalities to describe

the values

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

Increasing, Decreasing, or Constant

• Sweep from left to right and notice what happens to the y-values

• Increasing goes up (L to R)• Decreasing falls down (L to R)• Constant is a horizontal graph

Picture Example

Example:

Continuous vs Discontinuous

• Continuous has NO breaks

• Discontinuous has gaps or breaks

Picture Example of Continuous

Picture Example of Discontinuous

Discrete Function  -  A function that is defined only for a set of numbers that can be listed, such as the set of whole numbers or the set of integers. (The points are not connected

Extrema•Minimum Point – least value of the function. Lowest Point.

•Maximum Point – greatest value of the function. Highest Point

Picture Example

Example

Domain & Range

• Domain – all x-values of a function

• Range – all y-values of a function

Picture Example

Ecample

AsymptoteA line that a graph gets closer and closer to, but never crosses or touches

Example

Characteristics1. Domain:

2. Range:3. Intercepts:4. Increasing

or Decreasing?

5. Maximum or Minimum?

Characteristics

1. Domain:2. Range:3. Intercepts:4. Increasing or

Decreasing?5. Maximum or

Minimum?6. Horizontal

Asymptote:

ClassworkCharacteristics of

FunctionsWorksheet 5

problems

HomeworkCharacteristics of

FunctionsWorksheet 6

problems