Final answer:
To prove that a function is not a linear transformation, we need to find a counterexample where the function does not satisfy the properties of a linear transformation.
Step-by-step explanation:
A linear transformation is a function that preserves vector operations, such as addition and scalar multiplication. To prove that a function is not a linear transformation, we need to find at least one counterexample where the function does not satisfy the properties of a linear transformation.
For example, let's consider a function f(x) = x^2. If we take two vectors, a and b, and multiply them by a scalar, c, the function should return the same result as multiplying the vectors by the scalar before applying the function. However, if we test f(ca) = (ca)^2 and cf(a) = c^2 * a^2, we can see that these two expressions are not equal. Therefore, the function f(x) = x^2 is not a linear transformation.
By finding such a counterexample where the properties of a linear transformation are not satisfied, we can prove that the function is not a linear transformation.