Domain and Range graphing task cards

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 (x) that will not cause any undefined behavior in the function.

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 (y) that result from using the domain values in the function.

Front

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

Back

To determine the domain from a graph, identify all the x-values that the graph covers. Any x-value that has a corresponding y-value is included in the domain.

Front

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

Back

To determine the range from a graph, identify all the y-values that the graph covers. Any y-value that corresponds to an x-value in the domain is included in the range.

Front

What does it mean if a function has a restricted domain?

Back

A restricted domain means that certain x-values are not included in the domain due to undefined behavior, such as division by zero or taking the square root of a negative number.

Front

What is an example of a function with a restricted domain?

Back

The function f(x) = 1/(x-2) has a restricted domain because x cannot equal 2, as it would make the denominator zero.

Front

What is an example of a function with a restricted range?

Back

The function f(x) = x^2 has a restricted range of [0, ∞) because the output (y-values) cannot be negative.

Front

How can you find the domain of a polynomial function?

Back

The domain of a polynomial function is all real numbers, as polynomials do not have restrictions like division by zero or square roots of negative numbers.

Front

What is the significance of the x-intercept in relation to the domain?

Back

The x-intercept indicates where the function crosses the x-axis, and it is part of the domain as long as it is defined.

Front

What is the significance of the y-intercept in relation to the range?

Back

The y-intercept indicates where the function crosses the y-axis, and it is part of the range as long as it is defined.