Determining Functions on Graphs

The video tutorial explains how to determine if a line on a graph represents a function by mapping inputs to outputs. It covers the concept of ordered pairs, the definition of a function, and the use of the vertical line test to identify functions. The tutorial also addresses common misconceptions about horizontal line tests and analyzes different graph types, such as circles and lines, to determine their function properties.

What is the primary characteristic of a function in terms of inputs and outputs?

• Each input can have multiple outputs.

• Each input has exactly one output.

• Each output can have multiple inputs.

• Each output has exactly one input.

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

• Horizontal line test

• Diagonal line test

• Parallel line test

• Vertical line test

Why is it incorrect to use a horizontal line test to determine if a graph is a function?

• Because it checks for multiple outputs for a single input.

• Because it checks for multiple inputs for a single output.

• Because it only works for linear graphs.

• Because it is not a recognized mathematical test.

If a graph shows a car's speed at different times, and the speed is the same at two different times, is it a function?

• No, because the graph is not linear.

• Yes, because the speed can vary over time.

• No, because the speed is the same at different times.

• Yes, because each time has one speed.

In the context of functions, what does it mean if a vertical line touches a graph at more than one point?

• The graph does not represent a function.

• The graph is a quadratic function.

• The graph represents a function.

• The graph is a linear function.

What is the result of applying the vertical line test to a circle on a graph?

• The circle is not a function.

• The circle is a quadratic function.

• The circle is a function.

• The circle is a linear function.

What does it indicate if a vertical line touches a graph at exactly one point?

• The graph is not a function.

• The graph is a function.

• The graph is a quadratic function.

• The graph is a cubic function.