Math Problem Statement
Using the graphs of y = f(x) and y = g(x), evaluate the following:
a) f(1)
b) g(-2)
c) f(4) - g(-2)
d) x when f(x) = -3
Solution
Let’s evaluate the given values using the graphs provided.
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Evaluate :
- From the graph of (the one on the left), look at the value of the function when .
- The point corresponding to on the graph of is , so:
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Evaluate :
- From the graph of (the one on the right), look at the value of the function when .
- The point corresponding to on the graph of is , so:
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Evaluate :
- From the graph of , there is no point corresponding to (since the function isn't defined beyond ). Thus, is undefined.
- For , as found earlier, .
- So, the expression cannot be evaluated because is undefined.
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Find when :
- From the graph of , find the value of where .
- From observation, the point where occurs at .
- Thus, when .
Summary:
- a)
- b)
- c) is undefined.
- d) when .
Would you like further details or clarifications?
Here are 5 related questions to consider:
- What is the value of from the graph?
- What is the domain of the function ?
- For which values of does ?
- Is the function continuous for all ?
- How would you describe the behavior of as ?
Tip: When reading graphs, always pay attention to the scale and the defined domain to avoid misinterpretations!
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Math Problem Analysis
Mathematical Concepts
Graph Reading
Function Evaluation
Basic Algebra
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9