Domain & 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 does the vertical line test determine?

Back

Whether a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

If a function has a domain of 1 ≤ x ≤ 4, what does this mean?

Back

The input values (x) can range from 1 to 4, inclusive.

Front

If a function has a range of y ≥ -1, what does this indicate?

Back

The output values (y) start from -1 and go to positive infinity.

Front

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

Back

x ≥ 1, since the expression under the square root must be non-negative.

Front

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

Back

y ≥ 0, since the square of any real number is non-negative.

Front

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

Back

Identify the lowest and highest y-values that the graph reaches.

Front

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

Back

x ≠ 2, since the function is undefined at x = 2.

Front

What does it mean if a function is defined as f: R → R?

Back

The function takes any real number as input and produces a real number as output.