Use the graphs of f and g to solve Exercises 83–90.

Find (fg) (2).

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Step 1: Understand the problem. You are tasked with finding (fg)(2), which means you need to evaluate the product of the functions f(x) and g(x) at x = 2.

Step 2: Locate x = 2 on the graph. Look at the horizontal axis and find the point where x = 2.

Step 3: Determine the value of f(2). Find the red graph (representing f(x)) and identify the y-coordinate of the point where x = 2.

Step 4: Determine the value of g(2). Find the blue graph (representing g(x)) and identify the y-coordinate of the point where x = 2.

Step 5: Multiply the values of f(2) and g(2). Once you have the values of f(2) and g(2), multiply them together to find (fg)(2).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, if we have a function f(x), evaluating it at x = 2 means finding f(2). This is essential for solving problems that require specific outputs from given functions.

Product of Functions

The product of two functions, denoted as (fg)(x), is defined as the multiplication of their outputs at a given input x. Specifically, (fg)(x) = f(x) * g(x). To find (fg)(2), one must first evaluate f(2) and g(2), then multiply these results together.

Graph Interpretation

Interpreting graphs of functions involves analyzing the visual representation of the functions to extract information such as values at specific points. In this case, the graphs of f(x) and g(x) can be used to find f(2) and g(2) by locating the corresponding y-values at x = 2 on their respective graphs.

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In Exercises 77–92, use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any; and e. the missing function values, indicated by question marks, below each graph.

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Begin by graphing the absolute value function, f(x) = |x|. Then use transformations of this graph to graph the given function. h(x) = |x + 3| - 2

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Use the graphs of f and g to solve Exercises 83–90.

Find(g/f)(3)

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