Math Problem Statement

Select the domain and range of the function represented by the graph.

Solution

To determine the domain and range of the function represented by the graph, let's analyze the endpoints and behavior of the graph:

Domain:

The domain represents the set of all possible xx-values for which the function is defined.

  • The graph starts at x=2x = -2 on the left (open circle, meaning x=2x = -2 is not included).
  • The graph extends to x=3x = 3 on the right (closed circle, meaning x=3x = 3 is included).
  • Therefore, the domain is 2x3-2 \leq x \leq 3.

Range:

The range represents the set of all possible yy-values that the function takes.

  • The graph starts at y=2y = -2 (open circle, meaning y=2y = -2 is not included).
  • The graph extends to y=4y = 4 (closed circle, meaning y=4y = 4 is included).
  • Therefore, the range is 2<y4-2 < y \leq 4.

Now, let's look at the answer choices:

  • Option D: 2x3-2 \leq x \leq 3 and 1y4-1 \leq y \leq 4 doesn't include the lower bound correctly for the yy-values.
  • Option A: 2x3-2 \leq x \leq 3 and 2y4-2 \leq y \leq 4 matches the description, except the inequality y=2y = -2 is incorrect because it's an open circle at y=2y = -2.

Thus, the correct answer is Option A.

Would you like any additional details or clarifications?


Here are 5 related questions:

  1. What is the definition of domain and range in general?
  2. How do you interpret open and closed circles on a graph?
  3. What are other methods for finding the range of a function?
  4. How does one determine if a function is continuous from its graph?
  5. Can a function have a different domain than range?

Tip: Always check the endpoints of a graph carefully to see whether the points are included (closed circle) or excluded (open circle).

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Domain and Range
Function Graphs
Inequalities

Formulas

Domain: set of all possible x-values
Range: set of all possible y-values

Theorems

Understanding open and closed intervals based on graph endpoints

Suitable Grade Level

Grades 8-10