Domain and Range of Functions (Review)

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 linear function?

Back

The domain of a linear function is typically all real numbers unless specified by constraints such as inequalities.

Front

What is the range of the function f(x) = 2x + 3?

Back

The range is all real numbers, as a linear function can produce any y-value.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2, where the function is undefined.

Front

How do you find the range of a quadratic function?

Back

For a quadratic function in the form f(x) = ax^2 + bx + c, the range depends on the value of 'a'. If 'a' > 0, the range is [k, ∞) where k is the minimum value. If 'a' < 0, the range is (-∞, k] where k is the maximum value.

Front

What is the range of the function f(x) = -x^2 + 4?

Back

The range is (-∞, 4] because the maximum value is 4 when x = 0.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements, meaning each output is produced by exactly one input.

Front

How can you determine if a function is one-to-one using its graph?

Back

A function is one-to-one if any horizontal line intersects the graph at most once (Horizontal Line Test).

Front

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

Back

The domain is x ≥ 1, as the expression under the square root must be non-negative.