FUNCTIONS

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if no vertical line intersects the graph at more than one point.

Front

What does it mean for an input to repeat in a function?

Back

If an input (x-value) repeats, it means that there are multiple outputs (y-values) for that input, which violates the definition of a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function by checking if any vertical line crosses the curve more than once.

Front

What is a mapping in the context of functions?

Back

A mapping shows how each element from one set (domain) is paired with an element from another set (range).

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Is the following relation a function? {(1, 2), (1, 3), (2, 4)}

Back

No, because the input '1' is associated with two different outputs (2 and 3).

Front

Is the following relation a function? {(1, 2), (2, 3), (3, 4)}

Back

Yes, because each input is associated with exactly one output.