Understanding Functions and Their Behaviors

The video tutorial explains the concept of functions, including increasing, decreasing, and constant functions. It uses sets of ordered pairs to determine if they represent functions and describes their behavior. The vertical line test is introduced as a method to verify if a graph represents a function. Examples are provided with sets F, G, H, and J, illustrating different scenarios of function behavior and non-function cases.

What is a function in terms of input and output?

• A function has multiple outputs for each input.

• A function has exactly one output for each input.

• A function has the same output for all inputs.

• A function has no outputs for any input.

Which test can be used to determine if a graph represents a function?

• Horizontal Line Test

• Diagonal Line Test

• Vertical Line Test

• Circular Line Test

What does it mean if a function is increasing?

• As inputs decrease, outputs increase.

• As inputs increase, outputs also increase.

• As inputs increase, outputs remain constant.

• As inputs increase, outputs decrease.

In Set F, what indicates that it is a function?

• The graph fails the vertical line test.

• Each input is paired with exactly one output.

• The outputs are all the same.

• Each input is paired with multiple outputs.

Why does Set G not represent a function?

• It has no inputs.

• It has the same output for all inputs.

• It has multiple outputs for a single input.

• It has more inputs than outputs.

What happens at x = 1 in the graph of Set G?

• There are two points of intersection.

• There is exactly one point of intersection.

• The graph is a horizontal line.

• There is no point of intersection.

What is the behavior of Set H?

• It is not a function.

• It is a decreasing function.

• It is an increasing function.

• It is a constant function.

How can you describe the outputs in Set H?

• The outputs vary with each input.

• The outputs are all different.

• The outputs are all the same.

• The outputs decrease as inputs increase.

What is the behavior of Set J?

• It is not a function.

• It is a decreasing function.

• It is an increasing function.

• It is a constant function.

What does the graph of Set J indicate?

• The graph fails the vertical line test.

• The graph goes downhill from left to right.

• The graph is a horizontal line.

• The graph goes uphill from left to right.