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 y=2x+4y = 2^x + 4 assigns a unique yy-value to each xx-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:

  1. What is the difference between a relation and a function in general?
  2. How can you tell if a given equation represents a function?
  3. What is the range of the function y=2x+4y = 2^x + 4?
  4. How does the graph of y=2x+4y = 2^x + 4 look?
  5. What kind of transformations occur when comparing y=2xy = 2^x and y=2x+4y = 2^x + 4?

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