Excluded Values of Rational Expressions with Functions Concepts

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The set of all possible output values (y-values) that a function can produce.

Front

How do you find excluded values in rational expressions?

Back

Excluded values are found by setting the denominator equal to zero and solving for x.

Front

What does it mean if a function is defined for x ≥ -3?

Back

It means that the function includes all values of x starting from -3 and going to positive infinity.

Front

What is the significance of the range -2 ≤ y ≤ 4?

Back

It indicates that the output values of the function can be any number between -2 and 4, inclusive.

Front

What is the difference between domain and range?

Back

Domain refers to input values (x), while range refers to output values (y) of a function.

Front

If a function has a domain of -7 ≤ x < 5, what does this imply?

Back

It means that x can take any value from -7 up to, but not including, 5.

Front

What is an example of a rational expression?

Back

An example is f(x) = (2x + 3) / (x - 1), where x cannot be 1.

Front

What are the excluded values for the function f(x) = 1/(x^2 - 4)?

Back

The excluded values are x = 2 and x = -2, since these make the denominator zero.

Front

How do you express the domain of a function given a set of points?

Back

The domain is expressed as the set of all x-values from the given points.