functions domain range

Front

What is the definition of the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

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

Back

To find the domain from a graph, look at the x-values covered by the graph from left to right.

Front

What is the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that the function can output.

Front

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

Back

To find the range from a graph, look at the y-values covered by the graph from the lowest point to the highest point.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

Identify the domain of the function f(x) = x^2.

Back

All real numbers.

Front

Identify the range of the function f(x) = x^2.

Back

y ≥ 0.

Front

What is an example of a function that is not a one-to-one function?

Back

f(x) = x^2, because multiple x-values (e.g., -2 and 2) produce the same y-value (4).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

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

Back

All real numbers except x = 0.