Math Problem Statement
Which statement is true about y = 2^x + 4? A; It represents a function only. B; It represents both a relation and a function. C; It represents neither a relation nor a function. D; It represents a relation only.
Solution
The correct answer is B: It represents both a relation and a function.
Explanation:
- A relation is any set of ordered pairs, where the first element is from the domain (input) and the second is from the range (output).
- A function is a specific type of relation where each input (x-value) is paired with exactly one output (y-value).
The equation assigns a unique -value to each -value. Therefore, it satisfies the definition of both a relation and a function.
Would you like more details or have any further questions?
Here are 5 related questions:
- What is the difference between a relation and a function in general?
- How can you tell if a given equation represents a function?
- What is the range of the function ?
- How does the graph of look?
- What kind of transformations occur when comparing and ?
Tip: To test if an equation represents a function, use the vertical line test on its graph. If a vertical line crosses the graph at only one point for all x-values, it is a function.
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Math Problem Analysis
Mathematical Concepts
Relations
Functions
Exponential Functions
Formulas
y = 2^x + 4
Theorems
Definition of Relation
Definition of Function
Vertical Line Test
Suitable Grade Level
Grades 9-12