Identify the domain and range of the following function. The rule is 𝑦 equals 𝑥 minus four and 𝑥 is the set nine, ten, eleven, and twelve.
Here’s a visual that helps us remember what exactly domain and range are. The domain is the set of all the input values or the 𝑥-values. The range is the set of all the output values, the 𝑦-values. We find the 𝑦-values or the range by taking the domain, the 𝑥-values, using the function rule to see what the outcome is.
In this problem, we’ve already been given the set of 𝑥-values, which means we’ve already been given the full domain. We’ll have to use the domain, put the domain into our function rule to find the range. We’re given the function rule 𝑦 equals 𝑥 minus four.
Let’s calculate the range. If we input a nine into our function rule, the output is five. Nine minus four equals five. This is one of our values for the range.
Next step, ten. Ten minus four equals six. Six is our next value for the range. We input eleven. Eleven minus four equals seven.
Seven is part of our range. Our last 𝑥-value is twelve. We input twelve into our function rule. Twelve minus four equals eight. Eight is included in the range.
If 𝑥 is the set nine, ten, eleven, twelve, then 𝑦 is the set five, six, seven, eight. The set of all our 𝑥-values is the domain. The set of all of our 𝑦-values is the range.