We are asked to write a nonlinear functionrule that fits the following description.
when d is 4, r is 9, and r is a function of d
Since we know that r is a function of d, we know that d is the independent variable. Since the independent variable of linear functions always has an exponent of 1, we can give d an exponent that is not 1 to ensure our function is not linear. Let's begin writing our rule by raising d to the power of 2.
r = d^2
To ensure that we satisfy the condition when d is 4, r is 9, we can substitute d= 4 into the right-hand side of the rule above. Let's write the next step in our partial equation.
r= d^2 ⇔ r= 4^2 ⇔ r=16
Our equation resulted in r=16. However, since we are told that r=9, we need to subtract 7 from the variable.
r = d^2 - 7
Note that this rule is just one example of a nonlinear function. There are infinitely many possible functions that can be created to satisfy the given conditions.
Checking Our Answer
Substituting the Given Value
We can substitute d=4 and r=9 into our function rule to verify that it satisfies the conditions.
