Domain Algebraically, Domain Range Interval Notation, Evaluate

Front

What is 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

How do you find the domain of a rational function?

Back

To find the domain of a rational function, identify values of x that make the denominator zero and exclude them from the domain.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation (a, b) represent?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

Front

What does the notation [a, b] represent?

Back

The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

Front

What is 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 evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the given value into the function's equation and simplify.

Front

What is the difference between domain and range?

Back

The domain refers to the input values of a function, while the range refers to the output values.

Front

How do you express the domain of the function f(x) = \frac{x + 7}{x^2 - 6x + 8}?

Back

The domain is expressed as \left(-\infty, 2\right) \cup \left(2, 4\right) \cup \left(4, \infty\right).

Front

How do you find the domain of the function f(x) = \sqrt{8x + 40}?

Back

Set the expression inside the square root greater than or equal to zero: 8x + 40 \geq 0, which gives the domain as \left[-5, \infty\right).