Key Features of Functions

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

What does it mean for a function to have a maximum?

Back

A function has a maximum if there is a highest point on its graph, where the function value is greater than or equal to all other values in its domain.

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, as the x-values increase, the y-values decrease.

Front

What is a y-intercept?

Back

The y-intercept of a function is the point where the graph intersects the y-axis, represented as (0, y).

Front

How do you find the domain of a function from its graph?

Back

To find the domain from a graph, identify all the x-values for which the graph has points.

Front

How do you find the range of a function from its graph?

Back

To find the range from a graph, identify all the y-values that the graph reaches.

Front

What is an example of a function with no maximum?

Back

A function like f(x) = x^2 has no maximum because it continues to increase indefinitely.

Front

What is an example of a decreasing interval in a function?

Back

In the function f(x) = -x + 2, it is decreasing on the interval (-∞, 2).

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept can represent the starting value of a situation in real-world problems, such as initial cost or starting population.