Functions!

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

How can you determine if a table of values represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed; its rate of change varies.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

What is the definition of a mapping in the context of functions?

Back

A mapping is a way to describe how each element of one set (domain) is paired with an element of another set (range).

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's equation and simplify.

Front

What is the output of the function f(x) = x + 5 when x = 2?

Back

The output is 7, since f(2) = 2 + 5.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function has a variable rate of change and does not graph as a straight line.