Domain: All real numbers
Range: All real numbers
It is a function.
It is neither one-to-one nor onto.
If f(x)=−2x+3:
f(−2)=7
f(4)=−5
f(6)=−9
The domain of a relation refers to the set of all possible input values (x-values), while the range represents the set of all possible output values (y-values). In the given table, the domain consists of all real numbers, and the range includes all real numbers as well. This is because there is a y-value associated with every x-value, and vice versa, indicating that the relation covers the entire real number line.
To determine if the relation is a function, we assess whether each x-value is associated with a unique y-value. In this case, there are no repeated x-values with different y-values, confirming that it is indeed a function.
However, the function is neither one-to-one nor onto. A one-to-one function would mean that each unique x-value maps to a unique y-value, which is not the case here. An onto function would imply that the range covers all possible y-values, but there are missing y-values in this relation.
Next, if f(x)=−2x+3, we can find specific function values:
f(−2)=−2(−2)+3=7
f(4)=−2(4)+3=−5
f(6)=−2(6)+3=−9
These values represent the corresponding y-values for the given x-values in the function.