Exploring Features of Functions

This video tutorial covers the concept of functions in mathematics, including their definition, examples, and how to determine if a graph represents a function using the vertical line test. The lesson includes an activity to practice identifying functions and explains key vocabulary such as x-intercept, y-intercept, relative maximum, and minimum. The tutorial also provides guidance on analyzing graphs to determine intervals of increase and decrease, as well as domain and range. The session concludes with practice exercises to reinforce the concepts learned.

What is the basic definition of a function?

• Each x value has multiple y values

• Each x value has only one y value

• Each y value has multiple x values

• Each y value has only one x value

Which of the following is an example of a linear function?

• y = log(x)

• y = 3x + 8

• y = 2^x

• y = x^2 + 2

What does the vertical line test determine?

• If a graph is quadratic

• If a graph represents a function

• If a graph is exponential

• If a graph is linear

In the vertical line test, what indicates that a graph is not a function?

• The vertical line is horizontal

• The vertical line does not cross the graph

• The vertical line crosses the graph at multiple points

• The vertical line crosses the graph at one point

When looking at a table, how can you tell if it represents a function?

• If all x values are different

• If all y values are the same

• If x values repeat with different y values

• If y values repeat with different x values

What does a closed circle on a graph indicate?

• The value is included

• The graph is linear

• The value is not included

• The graph is not a function

What is the x-intercept of a graph?

• The lowest point on the graph

• The highest point on the graph

• Where the graph crosses the x-axis

• Where the graph crosses the y-axis

What is the relative maximum of a graph?

• The lowest point on the graph

• The point where the graph crosses the x-axis

• The highest point on the graph

• The point where the graph crosses the y-axis

What does the domain of a function represent?

• The highest y value

• All possible x values

• The lowest x value

• All possible y values

What does the range of a function represent?

• The highest x value

• The lowest y value

• All possible x values

• All possible y values