Question

select the correct answer. which statement is true about this equation? $y = 2^x + 4$ a. it represents a relation only. b. it represents both a relation and a function. c. it represents neither a relation nor a function. d. it represents a function only.

Explanation:

Step1: Recall definitions

A relation is a set of ordered pairs \((x,y)\) where \(x\) is from the domain and \(y\) from the range. A function is a relation where each \(x\) has exactly one \(y\).

Step2: Analyze \(y = 2^x + 4\)

For any real \(x\), plugging in \(x\) gives one \(y\) (by exponent and addition rules). So it's a function. Since all functions are relations (as functions are subsets of relations), it's both a relation and a function.

Answer:

B. It represents both a relation and a function.