Domain and Range of Functions

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 can you determine the domain of a polynomial function?

Back

The domain of a polynomial function is all real numbers, as polynomials are defined for every real number.

Front

What restrictions might affect the domain of a rational function?

Back

The domain of a rational function is restricted by values that make the denominator equal to zero.

Front

How do you find the range of a quadratic function?

Back

The range of a quadratic function can be determined by identifying the vertex and the direction of the parabola (upward or downward).

Front

What is the significance of the vertex in determining the range of a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, which helps define the range.

Front

What is an example of a function with a restricted domain?

Back

The function f(x) = √x has a restricted domain of x ≥ 0, as square roots of negative numbers are not defined in the real number system.

Front

How can you graphically determine the domain of a function?

Back

You can graph the function and observe the x-values for which the graph exists.

Front

What is the relationship between the domain and range of a function?

Back

The domain consists of input values, while the range consists of output values; they are related through the function's rule.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is all real numbers except x = 3, where the function is undefined.