Math Problem Statement

Use the graph of y = g(x) to find: a) g(0), b) g(-1), c) The domain, d) The range.

Solution

Let's go through the problem based on the graph you provided:

The graph represents y=g(x)y = g(x), and you need to find the following:

a) g(0)g(0)

Look for where x=0x = 0 on the graph. The corresponding value of yy at x=0x = 0 is approximately 1.

So, g(0)=1g(0) = 1.

b) g(1)g(-1)

Look for where x=1x = -1 on the graph. The corresponding value of yy at x=1x = -1 is approximately 0.

So, g(1)=0g(-1) = 0.

c) The domain

The domain represents all the possible values of xx. From the graph, the function appears to be defined for all xx between -5 and 3 (inclusive), so:

The domain is [5,3][-5, 3].

d) The range

The range represents all the possible values of yy. From the graph, the lowest point is y=5y = -5 and the highest point is y=3y = 3. Thus:

The range is [5,3][-5, 3].


Summary of the answers:

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

Would you like more details on any part of this? Here are some related questions to expand your understanding:

  1. How do you determine the domain of a function from its graph?
  2. What is the process for finding a function's range from a graph?
  3. How would the answers change if the graph had open endpoints?
  4. What are some real-world examples where functions like this might apply?
  5. How can you use transformations to modify the graph of g(x)g(x)?

Tip: Always check if there are any breaks or holes in a graph when determining the domain and range.

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Math Problem Analysis

Mathematical Concepts

Function Evaluation
Domain and Range
Graph Interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-11