Algebraically Determining Domain of Functions (1.1)

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 determine the domain of a rational function?

Back

To determine the domain of a rational function, identify values of x that make the denominator zero, as these values are excluded from the domain.

Front

What is the domain of the function f(x) = (x + 7) / (x^2 - 6x + 8)?

Back

The domain is (-∞, 2) ∪ (2, 4) ∪ (4, ∞). Values x = 2 and x = 4 are excluded because they make the denominator zero.

Front

What is the domain of the function f(x) = (x^2 + 5x - 6) / (x^2 + 10x + 24)?

Back

The domain is (-∞, -6) ∪ (-6, -4) ∪ (-4, ∞). Values x = -6 and x = -4 are excluded.

Front

How do you find the domain of a square root function?

Back

For a square root function, set the expression inside the square root greater than or equal to zero and solve for x.

Front

What is the domain of the function f(x) = √(8x + 40)?

Back

The domain is [-5, ∞). The expression 8x + 40 must be greater than or equal to zero.

Front

What is the domain of the polynomial function f(x) = x^2 - 6x + 8?

Back

The domain is (-∞, ∞). Polynomial functions are defined for all real numbers.

Front

What is the domain of the function f(x) = (x - 5) / (x^2 - 6x)?

Back

The domain is (-∞, 0) ∪ (0, 6) ∪ (6, ∞). Values x = 0 and x = 6 are excluded.

Front

What is a vertical asymptote in relation to the domain of a function?

Back

A vertical asymptote occurs at values of x that make the denominator of a rational function zero, indicating that the function approaches infinity.

Front

What is the significance of finding the domain of a function?

Back

Finding the domain is crucial for understanding the valid input values for a function, which affects its graph and behavior.