Key Features of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the domain of a function?

Back

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

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the output value at the second point is greater than the output value at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the output value at the second point is less than the output value at the first point.

Front

What is a maximum point of a function?

Back

A maximum point is a point on the graph of a function where the function value is greater than or equal to the function values at nearby points.

Front

What is a minimum point of a function?

Back

A minimum point is a point on the graph of a function where the function value is less than or equal to the function values at nearby points.

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts, set the output (y) to zero and solve for the input (x).

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept, set the input (x) to zero and solve for the output (y).

Front

What is an interval of positivity for a function?

Back

An interval of positivity is a range of x-values where the function outputs positive values (y > 0).