Domain and Range

Front

What is the domain of a function?

Back

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 set of all possible output values (y-values) that a function can produce.

Front

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

Back

Identify the x-values for which the graph exists; any x-value that results in a point on the graph is included in the domain.

Front

What does it mean if a function has a domain of x > -4?

Back

The function is defined for all real numbers greater than -4.

Front

What does it mean if a function has a range of f(x) < 9?

Back

The output values of the function are all real numbers less than 9.

Front

How can you represent the domain of a function using inequalities?

Back

You can use inequalities to express the limits of the input values, such as x > 0 or -1 < x < 5.

Front

What is an example of a function with a domain of all real numbers?

Back

f(x) = x^2 is defined for all real numbers.

Front

What is an example of a function with a restricted domain?

Back

f(x) = 1/x is defined for all real numbers except x = 0.

Front

What is the significance of the maximum cargo weight in a real-world function?

Back

It defines the upper limit of the input values (number of containers) for which the function is valid.

Front

How do you find the range of a quadratic function like f(x) = 9 - x^2?

Back

Identify the vertex and the direction of the parabola; the range is determined by the maximum or minimum value.