Understanding Functions and Their Properties

The video tutorial introduces relations and functions, explaining that a function is a special type of relation where each input is paired with exactly one output. It demonstrates how to identify functions using tables, ordered pairs, and graphs, including the vertical line test. The video also covers the behavior of function graphs, such as increasing, decreasing, and constant functions, and defines dependent and independent variables.

What is a function in the context of relations?

• A set of ordered pairs with no outputs

• A set of ordered pairs with exactly one output for each input

• A set of ordered pairs with multiple outputs for each input

• A set of ordered pairs with multiple inputs for each output

In a table of values, how can you identify a function?

• Each input is paired with multiple outputs

• Each input is paired with exactly one output

• Each output is paired with multiple inputs

• Each output is paired with exactly one input

What indicates a problem point in a graph of ordered pairs?

• An input paired with multiple outputs

• An input paired with no outputs

• An output paired with no inputs

• An output paired with multiple inputs

What does the vertical line test determine?

• If a graph is a line

• If a graph is a circle

• If a graph is increasing

• If a graph represents a function

What does it mean if a vertical line intersects a graph at more than one point?

• The graph is not a function

• The graph is a function

• The graph is a circle

• The graph is a line

What is the behavior of a function graph that is increasing?

• The graph goes uphill from left to right

• The graph forms a circle

• The graph remains constant

• The graph goes downhill from left to right

What is a constant function?

• A function where inputs remain the same regardless of outputs

• A function where outputs remain the same regardless of inputs

• A function where outputs decrease as inputs increase

• A function where outputs increase as inputs increase

What is the dependent variable in a function?

• The variable that is independent of the output

• The variable that remains constant

• The variable that depends on the input

• The variable that controls the input

Which of the following is true for a decreasing function?

• As inputs decrease, outputs increase

• As inputs decrease, outputs remain constant

• As inputs increase, outputs decrease

• As inputs increase, outputs increase

How can you describe the relationship between x and y in a function?

• y is a function of x

• x is a function of y

• x and y are unrelated

• x and y are independent