Use the graph to evaluate each expression. See Example 3(a).
(ƒg)(0)

Verified step by step guidance

1. Understand that (ƒg)(0) means the composition of functions ƒ and g evaluated at 0, which is written as ƒ(g(0)).
2. First, find the value of g(0) by locating x = 0 on the g(x) graph (blue line) and reading the corresponding y-value.
3. Next, take the value found for g(0) and use it as the input for the function ƒ. This means you will find ƒ(g(0)) by locating x = g(0) on the ƒ(x) graph (red curve) and reading the corresponding y-value.
4. Write the expression for the composition: (ƒg)(0) = ƒ(g(0)) and substitute the values you found from the graph.
5. The final step is to interpret the y-value from the ƒ graph at x = g(0) as the result of (ƒg)(0).

Key Concepts

Function Composition

Function composition involves applying one function to the result of another, denoted as (f∘g)(x) = f(g(x)). To evaluate (f∘g)(0), first find g(0), then substitute that value into f. This process combines two functions into a single operation.

Reading Values from a Graph

To evaluate functions using a graph, locate the input value on the x-axis and find the corresponding y-value on the function's curve. This y-value represents the function's output for that input. Accurate reading is essential for correct evaluation.

Understanding Quadratic and Linear Functions

The graph shows f(x) as a quadratic function (parabola) and g(x) as a linear function (straight line). Recognizing their shapes helps in interpreting values and behavior, such as f(x) having a minimum point and g(x) increasing steadily.