Domain and Range EOC Review

Front

What is the definition of Domain in 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

What is the definition of Range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

Front

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

Back

The domain can be determined by identifying the x-values for which the graph has points. It includes all x-values that the function can take.

Front

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

Back

The range can be determined by identifying the y-values that the graph reaches. It includes all y-values that the function can output.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is all real numbers except x = 3, since the function is undefined at that point.

Front

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

Back

The range is y ≥ 0, since the output of a square function is always non-negative.

Front

What does a horizontal translation of a function mean?

Back

A horizontal translation shifts the graph of a function left or right on the coordinate plane. For example, g(x) = f(x - 2) shifts f(x) 2 units to the right.

Front

What does a vertical translation of a function mean?

Back

A vertical translation shifts the graph of a function up or down. For example, g(x) = f(x) + 3 shifts f(x) up by 3 units.

Front

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

Back

The domain is x ≥ 0, since the square root function is only defined for non-negative values.

Front

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

Back

The range is y ≤ 0, since the output of a negative square function is always non-positive.