Domain and Range

Front

What is the definition of Domain in a function?

Back

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 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 has points; these values make up the domain.

Front

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

Back

Identify the y-values that the graph reaches; these values make up the range.

Front

What is the domain of the function f(x) = √(x - 1)?

Back

x must be greater than or equal to 1, so the domain is [1, ∞).

Front

What is the range of the function f(x) = x^2?

Back

The range is all real numbers greater than or equal to 0, so [0, ∞).

Front

Given the function f(x) = 3x + 2, what is its domain?

Back

All real numbers, as there are no restrictions on x.

Front

Given the function f(x) = 1/(x - 2), what is its domain?

Back

All real numbers except x = 2, so (-∞, 2) ∪ (2, ∞).

Front

What is the range of the function f(x) = -x^2?

Back

The range is all real numbers less than or equal to 0, so (-∞, 0].

Front

How do you find the range of a quadratic function in vertex form?

Back

Identify the vertex; if the parabola opens upwards, the range starts from the y-coordinate of the vertex.