Domain and Range from Equations

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 function involving a square root?

Back

The domain of a function involving a square root is determined by setting the expression inside the square root greater than or equal to zero.

Front

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

Back

The domain is all real numbers except x = 1, since the function is undefined at that point.

Front

What is the range of the function f(x) = 3 - √x?

Back

The range is (-∞, 3], as the square root function produces non-negative values, and subtracting from 3 gives values up to 3.

Front

What is the domain of the function f(x) = 2 + √(3x - 1)?

Back

The domain is [1/3, ∞), since 3x - 1 must be greater than or equal to zero.

Front

What is the domain of the function f(x) = 2 + √(3x - 3)?

Back

The domain is [1, ∞), since 3x - 3 must be greater than or equal to zero.

Front

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

Back

The domain is [0, ∞), since the square root function is defined for non-negative values.

Front

What is the significance of vertical asymptotes in determining the domain of a function?

Back

Vertical asymptotes indicate values of x where the function is undefined, thus they must be excluded from the domain.

Front

How do you find the range of a function algebraically?

Back

To find the range, solve the equation for y and determine the possible values of y based on the function's behavior.