Domain and Range

Front

What is the definition of 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 definition of 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 the domain of a function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists, including any restrictions such as holes or vertical asymptotes.

Front

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

Back

The range can be determined by identifying the y-values that the graph reaches, including any restrictions such as horizontal asymptotes.

Front

What does the notation {x | -∞ < x < +∞} represent?

Back

This notation represents the domain of all real numbers, meaning any real number can be an input.

Front

What does the notation {y | -6 ≤ y ≤ 3} represent?

Back

This notation represents the range of the function, indicating that the output values (y) are between -6 and 3, inclusive.

Front

What is the domain of the function defined by the inequality -7 ≤ x < 5?

Back

The domain includes all real numbers x such that -7 is less than or equal to x and x is less than 5.

Front

What is the range of the function defined by the inequality -2 ≤ y ≤ 10?

Back

The range includes all real numbers y such that y is greater than or equal to -2 and less than or equal to 10.

Front

What is the significance of closed and open intervals in domain and range?

Back

Closed intervals include the endpoints (e.g., [a, b]), while open intervals do not include the endpoints (e.g., (a, b)). This affects whether certain values are included in the domain or range.

Front

How can you express the domain of a function using interval notation?

Back

The domain can be expressed in interval notation, such as (-∞, 5) for all x less than 5, or [-3, 3) for x between -3 and 3, including -3 but not 3.