In Exercises 91–94, use the graphs of f and g to evaluate each composite function.
(fog) (-1)

Verified step by step guidance

1. Identify the value of g(-1) from the graph of y = g(x).
2. Locate the point on the graph of y = g(x) where x = -1.
3. Read the corresponding y-value for this point, which is g(-1).
4. Use the value of g(-1) as the input for the function f.
5. Find the value of f(g(-1)) by locating the point on the graph of y = f(x) where x equals g(-1) and read the corresponding y-value.

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 from Graphs

Evaluating functions from graphs involves determining the output value of a function for a specific input by locating the input on the x-axis and finding the corresponding output on the y-axis. This process is essential for understanding how functions behave visually and for calculating composite functions using their graphical representations.

Interpreting Graphs of Functions

Interpreting graphs of functions requires understanding the relationship between the x and y coordinates represented in the graph. Each point on the graph corresponds to an input-output pair, allowing for visual analysis of function properties such as continuity, increasing/decreasing behavior, and intercepts, which are crucial for evaluating composite functions.