Domain and Range of Graphs

Front

What is the domain of a function?

Back

The set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The set of all possible output values (y-values) that a function can produce.

Front

How do you determine the domain of a graph?

Back

Identify the x-values for which the graph exists; look for restrictions such as vertical asymptotes or holes.

Front

How do you determine the range of a graph?

Back

Identify the y-values that the graph reaches; look for horizontal asymptotes or the highest and lowest points.

Front

What does it mean if the domain is 'All real numbers'?

Back

The function is defined for every possible x-value without any restrictions.

Front

What does it mean if the range is 'y ≥ -6'?

Back

The function produces output values starting from -6 and going upwards, including -6.

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

Back

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

Front

If a graph has a domain of -6 ≤ x ≤ 6, what does this indicate?

Back

The function is only defined for x-values between -6 and 6, inclusive.

Front

What is a vertical line test?

Back

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