Math Problem Statement

State the domain and range for each graph and then tellif the graph is a function (wite yes or no). In set builder notation

Solution

The graph you've provided is a horizontal line at y=2y = 2.

Domain and Range:

  1. Domain: The domain of the graph is all the possible values of xx. Since the line extends infinitely in both the positive and negative directions along the x-axis, the domain is: Domain={xxR}\text{Domain} = \{ x \mid x \in \mathbb{R} \} This means that xx can be any real number.

  2. Range: The range is all the possible values of yy. Since the line is horizontal at y=2y = 2, the range is: Range={yy=2}\text{Range} = \{ y \mid y = 2 \} This means that yy is always 2.

Function Status:

  • Is it a function? Yes, this graph is a function because for every value of xx, there is exactly one corresponding value of yy (which is 2 in this case).

Set Builder Notation:

  • Domain: {xxR}\{ x \mid x \in \mathbb{R} \}
  • Range: {yy=2}\{ y \mid y = 2 \}

Would you like more details on this, or do you have any other questions?

Here are some related questions to expand your understanding:

  1. What would the graph look like if the line was at y=5y = 5?
  2. How would the domain and range change if the line was vertical instead of horizontal?
  3. Can you provide an example of a graph that is not a function?
  4. What is the significance of a graph passing the vertical line test?
  5. How would the domain and range be different for a parabolic graph y=x2y = x^2?

Tip: The vertical line test is a quick way to determine if a graph represents a function—if any vertical line crosses the graph more than once, it's not a function!

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Math Problem Analysis

Mathematical Concepts

Functions
Graphing
Set Builder Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12