Math Problem Statement

Use the graphs of the functions y = f(x) and y = g(x) to evaluate the combined functions.

(f/g)(2)

Use the graphs of the functions y = f(x) and y = g(x) to evaluate the combined functions (f/g)(2).

Solution

To evaluate (fg)(2)\left(\frac{f}{g}\right)(2), we need to use the graphs of the functions f(x)f(x) and g(x)g(x) to find their values at x=2x = 2, and then compute the quotient f(2)g(2)\frac{f(2)}{g(2)}.

From the graph:

  • The blue line represents f(x)f(x). At x=2x = 2, it looks like f(2)=4f(2) = 4.
  • The red line represents g(x)g(x). At x=2x = 2, it appears that g(2)=2g(2) = -2.

Now, we can calculate the quotient:

(fg)(2)=f(2)g(2)=42=2\left(\frac{f}{g}\right)(2) = \frac{f(2)}{g(2)} = \frac{4}{-2} = -2

Thus, (fg)(2)=2\left(\frac{f}{g}\right)(2) = -2.

Would you like further details, or do you have any other questions? Here are a few related questions you may find helpful:

  1. How do you calculate (f+g)(x)(f + g)(x) from graphs of functions?
  2. What are the properties of linear functions like f(x)f(x) and g(x)g(x)?
  3. How can you find the x- and y-intercepts from a linear graph?
  4. What is the significance of the point where f(x)f(x) and g(x)g(x) intersect?
  5. How can you determine the slope of a line from a graph?

Tip: When dealing with linear functions, pay close attention to the slopes and intercepts, as they provide essential information for determining the behavior of the function.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Graphing Linear Equations

Formulas

Quotient of functions: (f/g)(x) = f(x) / g(x)

Theorems

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Suitable Grade Level

Grades 8-10