In Exercises 91–94, use the graphs of f and g to evaluate each composite function.
(go f) (0)

Verified step by step guidance

1. Identify the value of f(0) from the graph of y = f(x).
2. Locate the point on the red graph where x = 0.
3. Read the corresponding y-value at x = 0 on the red graph to find f(0).
4. Use the value of f(0) as the input for the function g.
5. Find g(f(0)) by locating the y-value on the blue graph corresponding to the x-value f(0).

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, trace vertically to the graph of f, and read the output value. This skill is essential for determining the values needed for function composition.

Graph Interpretation

Interpreting graphs involves understanding the visual representation of functions, including their shapes, intersections, and behaviors. In this exercise, recognizing how the graphs of f and g interact helps in accurately determining the values needed for the composite function. This includes identifying key points and trends in the graphs.