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

(go f) (0)

Verified step by step guidance

1. Step 1: Understand the composite function (g ∘ f)(0). This means you first evaluate f(0) and then use the result as the input for g(x).
2. Step 2: Locate the value of f(0) on the graph of f(x) (red curve). Find the point where x = 0 and determine the corresponding y-value.
3. Step 3: Use the y-value obtained from f(0) as the input for g(x). Locate this value on the x-axis of the graph of g(x) (blue curve).
4. Step 4: Find the corresponding y-value on the graph of g(x) for the input obtained from Step 2.
5. Step 5: The final result of (g ∘ f)(0) is the y-value obtained from Step 4.

Key Concepts

Function Composition

Function composition involves combining two functions, where the output of one function becomes the input of another. In this case, the notation (g o f)(0) means to first evaluate f at 0, and then use that result as the input for g. Understanding this process is crucial for evaluating composite functions correctly.

Evaluating Functions from Graphs

To evaluate functions from their graphs, one must identify the corresponding output values for given input values. For instance, to find f(0), locate 0 on the x-axis of the graph of f and determine the corresponding y-value. This skill is essential for accurately performing function evaluations in composite functions.

Graph Interpretation

Interpreting graphs involves analyzing the visual representation of functions to extract information about their behavior, such as intercepts, slopes, and continuity. In this exercise, understanding how to read the graphs of f and g will help in determining the values needed for the composite function evaluation.