Homework 2 Domain and Range

Front

What is the definition of Domain in mathematics?

Back

The set of all possible input values (x-values) for a function.

Front

What is the definition of Range in mathematics?

Back

The set of all possible output values (y-values) for a function.

Front

What is the domain of a function that is defined for all real numbers?

Back

(-∞, ∞)

Front

What is the range of a parabola that opens upwards with its vertex at (0, 0)?

Back

y ≥ 0

Front

How do you determine the domain of a function from its graph?

Back

Identify the x-values for which the function is defined.

Front

How do you determine the range of a function from its graph?

Back

Identify the y-values that the function can take.

Front

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

Back

[1, ∞) because the expression under the square root must be non-negative.

Front

What is the range of the function f(x) = -x^2?

Back

(-∞, 0] because the maximum value is 0 at x = 0.

Front

If a function has a domain of [-1, ∞), what does this imply?

Back

The function is defined for all x-values starting from -1 and going to positive infinity.

Front

What is the domain of the function f(x) = 1/(x - 2)?

Back

(-∞, 2) ∪ (2, ∞) because x cannot equal 2.