Domain and Range

Front

What is the definition of 'domain' in 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 'range' in 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 that the graph covers, 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 covers, including any restrictions such as horizontal asymptotes.

Front

What does the notation (-∞, ∞) represent in terms of range?

Back

The notation (-∞, ∞) indicates that the range of the function includes all real numbers.

Front

What does the notation [a, b] signify in terms of domain?

Back

The notation [a, b] signifies that the domain includes all real numbers x such that a ≤ x ≤ b, including the endpoints a and b.

Front

What does the notation (a, b) signify in terms of domain?

Back

The notation (a, b) signifies that the domain includes all real numbers x such that a < x < b, excluding the endpoints a and b.

Front

What is the significance of vertical lines in a graph when determining the domain?

Back

Vertical lines can indicate restrictions in the domain, such as points where the function is undefined (e.g., vertical asymptotes or holes).

Front

What is the significance of horizontal lines in a graph when determining the range?

Back

Horizontal lines can indicate the maximum or minimum values of the function, helping to define the limits of the range.

Front

How can you express the range of a function that has a minimum value of -3 and no maximum?

Back

The range can be expressed as [-3, ∞) indicating that y can take any value greater than or equal to -3.