Continuous and Discrete

Front

What is the definition of a continuous function?

Back

A continuous function is a function where small changes in the input result in small changes in the output, meaning there are no breaks, jumps, or holes in the graph.

Front

What is the definition of a discrete function?

Back

A discrete function is a function that consists of distinct or separate values, often represented by individual points on a graph.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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

If the domain is (-inf, inf), what does it mean?

Back

It means that the function can accept any real number as an input.

Front

What does it mean if a function has a range of (-inf, inf)?

Back

It means that the function can produce any real number as an output.

Front

Can the x-values of a continuous function be all numbers?

Back

Yes, the x-values of a continuous function can be all real numbers.

Front

What type of graph represents a continuous function?

Back

A continuous graph, which is smooth and unbroken.

Front

What type of graph represents a discrete function?

Back

A discrete graph, which consists of separate points.

Front

Is the function f(x) = x^2 a continuous function?

Back

Yes, f(x) = x^2 is a continuous function.