Use the graphs of f and g to evaluate each composite function.

(fog) (-1)

Verified step by step guidance

1. Step 1: Understand the composite function (fog)(-1). This means we first evaluate g(-1) and then use that result as the input for f(x).
2. Step 2: Locate the value of g(-1) on the graph of g(x) (blue curve). Find the x-coordinate of -1 and determine the corresponding y-value.
3. Step 3: Use the y-value obtained from g(-1) as the input for f(x). Locate this value on the graph of f(x) (red curve) and determine the corresponding y-value.
4. Step 4: The final y-value obtained from f(g(-1)) is the result of the composite function (fog)(-1).
5. Step 5: Ensure all values are correctly read from the graph and verify the steps to avoid errors in interpretation.

Key Concepts

Composite Functions

A composite function is formed when one function is applied to the result of another function. It is denoted as (f ∘ g)(x), meaning f(g(x)). To evaluate a composite function, you first find the output of g for a given input, and then use that output as the input for f.

Function Evaluation

Function evaluation involves substituting a specific value into a function to determine its output. For example, if f(x) = 2x + 3, evaluating f(-1) means substituting -1 for x, resulting in f(-1) = 2(-1) + 3 = 1. This process is crucial for finding values in composite functions.

Graph Interpretation

Interpreting graphs of functions involves understanding how the visual representation relates to the function's behavior. For the functions f and g shown in the graph, one must identify the values of f and g at specific points, which aids in evaluating composite functions by tracing the outputs visually.