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

Let's analyze the two graphs shown in the image:

Left Graph:

  • Domain: The domain is the set of all possible x-values. The graph is a vertical line at x=3x = -3. Therefore, the domain is: {xx=3}\{ x \, | \, x = -3 \}

  • Range: The range is the set of all possible y-values. Since the vertical line extends infinitely in both directions along the y-axis, the range is all real numbers: {yyR}\{ y \, | \, y \in \mathbb{R} \}

  • Is it a function?: No, this graph is not a function. A vertical line test would show that multiple y-values correspond to the single x-value of 3-3, which violates the definition of a function.

Right Graph:

  • Domain: The domain is the set of all possible x-values. The graph is a single point at x=2x = 2. Therefore, the domain is: {xx=2}\{ x \, | \, x = 2 \}

  • Range: The range is the set of all possible y-values. The graph is a single point at y=3y = 3. Therefore, the range is: {yy=3}\{ y \, | \, y = 3 \}

  • Is it a function?: Yes, this graph is a function. Each x-value corresponds to exactly one y-value.

Would you like any further details or explanations?

Related Questions:

  1. What is the vertical line test, and how does it determine if a graph is a function?
  2. Can a single point on a graph ever not be a function?
  3. How does the domain differ when dealing with parabolas or quadratic functions?
  4. What happens to the domain and range when the graph of a function is shifted horizontally or vertically?
  5. What is the difference between a continuous and a discrete domain?

Tip:

When determining if a graph is a function, always remember that for each x-value, there should be only one corresponding y-value.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Vertical Line Test

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12