Determine if the given relations f, g, and h are functions. Provide reasons for your answers.

Alright sucess — let's do this. To understand if a relation is a function, remember two key rules: 1. Every element in the domain (the starting set, A) must be assigned to an element in the codomain (the target set, B). No element in A can be left out. 2. Each element in the domain must be assigned to exactly one element in the codomain. An element in A cannot have two different outputs in B. Given sets: A = \a, b, c, d\ and B = \r, s, t, u\. Step 1: Analyze relation f. The relation f is defined as: f(a) = s f(b) = u f(c) = t The element d A is not assigned to any element in B. This violates the first rule of functions. Is f a function?* ❌ No Reason:* The element d from the domain A is not defined (not assigned an image) in the codomain B. Step 2: Analyze relation g. The relation g is defined as: g(a) = s g(b) = u g(c) = u g(d) = t Every element in A (a, b, c, d) is assigned to exactly one element in B. For example, g(b)=u and g(c)=u is allowed; it just means two different inputs map to the same output. This satisfies both rules of functions. Is g a function?* ✅ Yes Reason:* Every element in the domain A is assigned to exactly one element in the codomain B. Step 3: Analyze relation h. The relation h is defined as: h(a) = s h(b) = u h(b) = t h(c) = u h(d) = t The element b A is assigned to two different elements in B: u and t. This violates the second rule of functions. Is h a function?* ❌ No Reason:* The element b from the domain A is assigned to two different images (u and t) in the codomain B. Here are the answers: f is not a function because f(d) is not defined. g is a function because every element of the source set A is assigned an image in the target set B, and each element in A has exactly one image. h is not a function because an element from the source set, b, has two different images (u and t) in the target set. Send me the next one 📸