Features of a 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, known as the domain.

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

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) corresponds to exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is the significance of the x-intercept in a function?

Back

The x-intercept indicates the values of x for which the function's output is zero, which can be important for solving equations.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs map to the same output.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function by checking if any vertical line intersects the graph at more than one point.

Front

What is an increasing function?

Back

An increasing function is a function where, as the input values increase, the output values also increase.