6.2 Cubic Domain & Range

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 is the domain and range of a cubic function?

Back

Domain: (-∞, ∞), Range: (-∞, ∞). All cubic functions can take any real number as input and produce any real number as output.

Front

How do you express the range of all cubic functions in inequality notation?

Back

-∞ < y < ∞.

Front

What is a restricted domain?

Back

A restricted domain is a subset of the domain of a function, limiting the input values to a specific interval.

Front

What is the domain of the function f(x) = (x - 1)(2x - 1)(x) when x > 0?

Back

Domain: (0, 0.5) ∪ (1, ∞). This means x can take values greater than 0 but not including 0.5 and 1.

Front

What is the range of the function f(x) = (x - 1)(2x - 1)(x) when x > 0?

Back

Range: (0, ∞). This means the output values of the function are all positive real numbers.

Front

What does it mean for a function to have a domain of all real numbers?

Back

It means that the function can accept any real number as an input without restrictions.

Front

What is the significance of interval notation?

Back

Interval notation is a way of writing subsets of real numbers, indicating the start and end points of the interval and whether they are included or excluded.

Front

How do you express the domain of a function that is restricted to [-3, 2]?

Back

Domain: [-3, 2]. This means x can take values from -3 to 2, including both endpoints.