Math Problem Statement

Use the graph of y = g(x) given above to find: a) g(-1) = ___ b) g(1) = ___ c) The domain: ___ d) The range: ___

Solution

Let's go through the graph and questions:

  1. g(-1):
    From the graph, find the value of the function g(x)g(x) when x=1x = -1. At x=1x = -1, the y-coordinate (function value) is approximately 0.

  2. g(1):
    Look at the graph at x=1x = 1. The function value at this point is 4.

  3. The domain:
    The domain refers to all the possible input values (x-values) for which the function is defined. Looking at the graph, the function is defined from x=2x = -2 to x=3x = 3. Hence, the domain is:
    Domain: [2,3][-2, 3].

  4. The range:
    The range refers to all the possible output values (y-values). From the graph, the lowest y-value is 0, and the highest y-value is 5. Hence, the range is:
    Range: [0,5][0, 5].

Summary of Answers:

  • a) g(1)=0g(-1) = 0
  • b) g(1)=4g(1) = 4
  • c) Domain: [2,3][-2, 3]
  • d) Range: [0,5][0, 5]

Would you like further details or explanations?

Here are 5 related questions to practice:

  1. What is g(0)g(0) from the graph?
  2. How would you find g(2)g(2) using the graph?
  3. Can a function have a domain that is not continuous?
  4. Explain the difference between domain and range in functions.
  5. How do you determine the maximum or minimum value of a function from its graph?

Tip: When determining the domain of a function, always look at the x-values covered by the graph, while for the range, examine the y-values.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Functions
Domain and Range

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9