Select the correct answer.

Which statement is true about this equation?
[tex]$y=2^z+4$[/tex]

A. It represents neither a relation nor a function.
B. It represents a relation only.
C. It represents a function only.
D. It represents both a relation and a function.

Question

Select the correct answer. 
 
Which statement is true about this equation? 
[tex]$y=2^z+4$[/tex] 
 
A. It represents neither a relation nor a function. 
B. It represents a relation only. 
C. It represents a function only. 
D. It represents both a relation and a function.

GinnyAnswer · Answer

The equation y = 2 z + 4 represents a set of ordered pairs, making it a relation. 
 For each value of z , there is only one corresponding value of y , satisfying the definition of a function. 
 Since the equation meets the criteria for both a relation and a function, it represents both. 
 Therefore, the correct answer is D ​ . 
 
 Explanation 
 
 Analyzing the Equation Let's analyze the given equation: y = 2 z + 4 . We need to determine whether this equation represents a relation, a function, or both. 
 
 Understanding Relations and Functions Recall the definitions of a relation and a function. A relation is simply a set of ordered pairs ( z , y ) that satisfy the equation. A function is a special type of relation where each input ( z in this case) has only one output ( y ). 
 
 Determining Uniqueness of Output For the given equation y = 2 z + 4 , we can choose any real number for z . For each value of z , we can calculate a unique value for y . This is because 2 z is a single, well-defined value for any real number z , and adding 4 to it will still result in a single, unique value for y . 
 
 Conclusion Since each input z produces only one output y , the equation represents a function. Also, since every function is a relation, the equation represents both a relation and a function.

Examples 
 Consider a scenario where you're tracking the growth of a bacteria population. The equation y = 2 z + 4 could model the number of bacteria ( y ) after z hours, assuming an initial population of 4 and exponential growth. Understanding functions helps predict how the population changes over time, which is crucial in fields like medicine and environmental science. This concept extends to various real-world applications, such as modeling compound interest, radioactive decay, and the spread of information.

Select the correct answer. Which statement is true about this equation? [tex]$y=2^z+4$[/tex] A. It represents neither a relation nor a function. B. It represents a relation only. C. It represents a function only. D. It represents both a relation and a function.

Answer (1)

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Select the correct answer.

Which statement is true about this equation?
[tex]$y=2^z+4$[/tex]

A. It represents neither a relation nor a function.
B. It represents a relation only.
C. It represents a function only.
D. It represents both a relation and a function.