Let's analyze the given equation [tex]\( y = 2^x + 4 \)[/tex].
### Definition of Relation and Function
1. Relation: A relation pairs each input value (from the domain) with output values (from the range). Essentially, any set of ordered pairs [tex]\((x, y)\)[/tex] can be considered a relation. As long as we have an x-value paired with a y-value, it is a relation.
2. Function: A function is a special kind of relation where each input value (x) is paired with exactly one output value (y). In other words, for every x in the domain, there is one and only one y in the range.
### Analysis
Given the equation [tex]\( y = 2^x + 4 \)[/tex]:
- Step 1: The equation [tex]\( y = 2^x + 4 \)[/tex] involves the variable [tex]\( x \)[/tex] being exponentiated by 2 and then having 4 added to the result.
- Step 2: For each value of [tex]\( x \)[/tex], there is exactly one corresponding value of [tex]\( y \)[/tex]. This means if you plug in a particular value of [tex]\( x \)[/tex], you'll always get a unique [tex]\( y \)[/tex].
Thus, because for every [tex]\( x \)[/tex] we have a unique [tex]\( y \)[/tex], this equation indeed represents a function.
- Step 3: Since any function is inherently a relation (it pairs values of [tex]\( x \)[/tex] with values of [tex]\( y \)[/tex]), we can confidently say that this represents both a relation and a function.
### Conclusion
Therefore, the correct statement about the equation [tex]\( y = 2^x + 4 \)[/tex] is:
- It represents both a relation and a function.
Answer: A
