Key Features of Functions Explored

The video tutorial explores key features of functions, focusing on graph analysis using Desmos. It covers interval notation, domain, range, intercepts, and graph behavior, including increasing, decreasing, and positive/negative sections. The tutorial also explains relative maxima, minima, zeros, and the average rate of change, providing a comprehensive understanding of function graphs.

What is interval notation used for?

• To find the intercepts of a graph

• To give boundaries for a set of numbers

• To describe the slope of a line

• To determine the average rate of change

Which symbol is used in interval notation to indicate that a number is included?

• Angle brackets

• Parentheses

• Brackets

• Curly braces

What does the domain of a function represent?

• The intercepts of the function

• The x-values of the function

• The y-values of the function

• The slope of the function

If a graph extends infinitely to the left, what is the domain notation?

• (-∞, ∞)

• (-∞, 0)

• (-∞, 0]

• [0, ∞)

Where does the y-intercept of a function occur?

• Where the graph crosses the x-axis

• Where the graph crosses the y-axis

• At the lowest point of the graph

• At the highest point of the graph

How many x-intercepts does the function in the video have?

• Four

• One

• Two

• Three

What does it mean when a graph is increasing?

• The graph is constant

• The graph is at its maximum

• The graph is moving upwards

• The graph is moving downwards

In which interval is the graph decreasing?

• From negative infinity to -1.155

• From -1.155 to 1.155

• From 1.155 to positive infinity

• From 0 to 2

When is a graph considered positive?

• When it is above the x-axis

• When it is on the x-axis

• When it is on the y-axis

• When it is below the x-axis

What is the average rate of change equivalent to?

• The intercepts of the function

• The domain of the function

• The range of the function

• The slope formula