Domain and Range Calculator

Find the Domain and Range of any Function: just plug in your function below, next press the arrow point right.

How do I use this Domain and Range Calculator?

Just enter your Function and press the blue “ARROW” button. The Domain and Range will be displayed above the arrow.

What are Domain and Range of a Function?

1) The Domain is defined as the set of all possible x-values that can be plugged into a function.
2) The Range of a function is defined as the set of all resulting y values.

Example: Find the Domain and Range of \( y = \sqrt(x-3) \) with Steps and Explanations.

1) The Domain is defined as the set of x-values that can be plugged into a function. In the above example, we can only plug in x-values greater or equal to 3 into the square root function avoiding the content of a square root to be negative.
Thus, Domain is \( x>=3 \) or \( [3,\infty ) \) in Interval Notation.

2) The Range of a function is defined as the set of all resulting y values. In the above example, the lowest y coordinate is y=0 achieved when x=3 is plugged in. The larger the x value plugged in the larger the y coordinate we obtain.
Thus, the Range is \( y>=0 \) or \( [0,\infty ) \) in Interval Notation.

What's another way to think of Domain and Range?

1) Domain are all possible x-values that can be plugged into a given function.
Ex: \( f(x)=1/x \) has Domain \( x \neq 0 \)
since x=0 makes the denominator zero and must therefore be excluded.

2) The Range are the y-values going from lowest (from the smallest y-value) to highest (to the largest y-value).
Ex: \( f(x)=x^2 - 5 \) has Range \( y >= -5 \)
since the y-values are above the parabola's mininum value of -5.

Ti-Nspire CX Calculator alert!

There is a built-in Domain() command that finds the Domain of any Function. No other TI calculator can do so. Not even the famous TI-84.

Watch this video on how to find Domain using the Ti-Nspire CX Calculator:

To find the Range and also the Domain of any Function, Ti-Nspire CX CAS users may simply use our Precalculus Made Easy APP at www.TinspireApps.com.

What are Domain and Range of a Constant Function?

Let's take the Example f(x)=6 which graphs a horizontal line with a y-intercept at 6.
1) The Domain is all real numbers as the function y=6 does not allow any input x. The Output is 6 regardless of the Input x.

2) The Range is just y=6. The lowest and highest y are both 6.

Is there a Video that helps me find the Domain and Range?

Yes of course. Watch this Khan Academy Video on how to solve Domain and Range Problems - Step by Step. In case of any remaining questions, please email us support@tinspireapps.com .