Identifying Functions Through Tables and Graphs

What is required for a relation to be considered a function?

• Each output must have only one input

• No two outputs can be the same

• Each input must have multiple outputs

• Each input must have exactly one output

What does the gumball machine analogy explain about functions?

• Each nickel can produce multiple gumballs

• Each nickel produces exactly one gumball

• Nickels and gumballs are unrelated

• Gumballs can vary depending on the nickel

Why can a function have inputs with the same output?

• It cannot; it violates function rules

• Only in graphical representations

• It's allowed as long as each input has one output

• Only if the inputs are also identical

How is function notation typically represented?

• x(f) = y

• f(x) = y

• y = x

• f = x(y)

In the provided table examples, what common feature did all functions share?

• All outputs were numbers

• Exactly one output for each input

• No outputs for some inputs

• Multiple outputs for one input

What is the correct function notation for a function of x?

• y(x) = f

• g(x) = y

• y = f(x)

• x = f(y)

What does the vertical line test determine about a graph?

• If the graph intersects the y-axis

• If the graph is a parabola

• If the graph represents a function

• If the graph is linear

What result from the vertical line test indicates that a graph is not a function?

• The line intersects the graph at one point

• The line intersects the graph at no points

• The line intersects the graph at more than one point

• The line does not touch the graph

What does an example of a function failing the vertical line test look like?

• A vertical line runs parallel to the y-axis

• A vertical line crosses at one point

• A vertical line does not touch the graph

• A vertical line crosses at two points

Which scenario correctly uses the vertical line test?

• Drawing a vertical line that intersects the graph at exactly one point

• Drawing a vertical line that does not intersect the graph

• Drawing a vertical line that touches the graph at multiple points

• Drawing a horizontal line across the graph