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.

  1. Evaluate f(1)f(1):

    • From the graph of f(x)f(x) (the one on the left), look at the value of the function when x=1x = 1.
    • The point corresponding to x=1x = 1 on the graph of f(x)f(x) is (1,1)(1, -1), so: f(1)=1f(1) = -1
  2. Evaluate g(2)g(-2):

    • From the graph of g(x)g(x) (the one on the right), look at the value of the function when x=2x = -2.
    • The point corresponding to x=2x = -2 on the graph of g(x)g(x) is (2,4)(-2, 4), so: g(2)=4g(-2) = 4
  3. Evaluate f(4)g(2)f(4) - g(-2):

    • From the graph of f(x)f(x), there is no point corresponding to x=4x = 4 (since the function isn't defined beyond x=2x = 2). Thus, f(4)f(4) is undefined.
    • For g(2)g(-2), as found earlier, g(2)=4g(-2) = 4.
    • So, the expression f(4)g(2)f(4) - g(-2) cannot be evaluated because f(4)f(4) is undefined.
  4. Find xx when f(x)=3f(x) = -3:

    • From the graph of f(x)f(x), find the value of xx where f(x)=3f(x) = -3.
    • From observation, the point where f(x)=3f(x) = -3 occurs at x=2x = -2.
    • Thus, x=2x = -2 when f(x)=3f(x) = -3.

Summary:

  • a) f(1)=1f(1) = -1
  • b) g(2)=4g(-2) = 4
  • c) f(4)g(2)f(4) - g(-2) is undefined.
  • d) x=2x = -2 when f(x)=3f(x) = -3.

Would you like further details or clarifications?

Here are 5 related questions to consider:

  1. What is the value of g(0)g(0) from the graph?
  2. What is the domain of the function f(x)f(x)?
  3. For which values of xx does g(x)=0g(x) = 0?
  4. Is the function f(x)f(x) continuous for all xx?
  5. How would you describe the behavior of g(x)g(x) as x4x \to 4?

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