Properties of Functions Review (1.1-1.2)

Front

What is the definition of a decreasing function?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

Front

What is the definition of an increasing function?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

How do you determine the range of a function from its graph?

Back

The range is determined by reading the graph from bottom to top, identifying the lowest and highest points on the y-axis.

Front

What does the interval notation (a, b) represent?

Back

The interval notation (a, b) represents all real numbers x such that a < x < b, excluding the endpoints a and b.

Front

What does the interval notation [a, b] represent?

Back

The interval notation [a, b] represents all real numbers x such that a ≤ x ≤ b, including the endpoints a and b.

Front

What is set notation?

Back

Set notation is a way to describe a set of numbers using a rule or condition, often written as { x | condition }.

Front

How do you express the interval (-∞, 5] in set notation?

Back

{ x | x ≤ 5 }.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints, while closed intervals do include their endpoints.

Front

What does it mean for a function to be constant on an interval?

Back

A function is constant on an interval if it takes the same value for every point in that interval.

Front

How can you identify intervals of increase and decrease from a graph?

Back

Intervals of increase are where the graph rises from left to right, and intervals of decrease are where the graph falls from left to right.