Final answer:
The student's question involves identifying whether a function is a linear transformation based on the two main properties of additivity and homogeneity of degree 1. The function is linear if it follows these properties, demonstrated by the provided equations showing straight lines when graphed. Without the specific function details, it isn't possible to identify which property it may fail.
The correct option is not given.
Step-by-step explanation:
The student has asked to determine if the function is a linear transformation and if not, which properties it fails to satisfy. A linear transformation must satisfy two main properties: Property 1 (additivity) and Property 2 (homogeneity of degree 1). The function is considered a linear transformation if for any vectors x and y in the domain and any scalar c, the following holds true:
- Property 1: T(x + y) = T(x) + T(y)
- Property 2: T(cx) = cT(x)
Without a specific function provided, we cannot determine which property is violated, if any. However, we can see examples of linear equations in practice question 1, where options A, B, and C are all linear equations, represented by the formula y = mx + b. This aligns with the definition of a linear transformation as they would satisfy both properties in a geometric sense, showing a straight line when graphed. If either property is not satisfied, the function is not a linear transformation.
The correct option is not given.