Unit 1A: Exploring Rates of Change

Lesson 1.1 - Functions and Function Notation

• A function describes the relationship between an independent and dependent variable.

• Each input is mapped to exactly one output. Independent = input (x) Dependent = output (y or f(x))

• To evaluate a function, find the output for a given input using a table, graph, or an equation.

Domain: The set of inputs of a function (x)

Range: The set of outputs for a function (y or f(x))

Lesson 1.2 - Interpreting Graphs of Functions

• A graph can show two quantities that vary with respect to each other.

• A function, f, is increasing on an interval of it’s domain if, as the input values increase, the output values increase as well.

  If a < b, then f(a) < f(b)

• A function, f, is decreasing on an interval of its domain if, as the input values increase, the output values decrease.

If a < b, then f(a) > f(b)

• X-intercepts, maximum, and minimum values, and intervals of increase or decease can reveal important info about a context.

Lesson 1.3 - Concavity

• If a graph has a positive slope, then the output is increasing. If a graph has a negative slope, then the output is decreasing. The value of the slope gives the rate of change

• Rate of change is increasing, then the graph is concave up (like a cup).

• Rate of change is decreasing, then the graph is concave down (like a frown).

• The point of inflection is where the concavity changes (steepest).