Determining Functions Using Tables and Graphs

This lesson teaches how to determine if relations are functions using tables and graphs. A function is defined as a relation where each input has exactly one output. The lesson uses examples, including a gumball machine analogy, to clarify misconceptions. Function notation is introduced, and the vertical line test is explained as a method to identify functions graphically. The lesson concludes by reinforcing the understanding of functions through tables and graphs.

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

• Each output must have exactly one input.

• Each output can have multiple inputs.

• Each input must have exactly one output.

• Each input can have multiple outputs.

In the context of functions, what does the notation f(x) represent?

• The output of a function.

• A constant value.

• The input of a function.

• A function of x.

How can you determine if a table represents a function?

• By checking if each input has exactly one output.

• By checking if each output has exactly one input.

• By ensuring all inputs are positive.

• By ensuring all outputs are negative.

What does the vertical line test help determine about a graph?

• If the graph is symmetrical.

• If the graph is a straight line.

• If the graph is a function.

• If the graph has a maximum point.

What indicates that a graph is not a function when using the vertical line test?

• A vertical line does not intersect the graph.

• A vertical line intersects the graph at more than one point.

• A vertical line intersects the graph at exactly one point.

• A vertical line intersects the graph at a tangent.