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

Verified step by step guidance

1. Identify the functions f(x) and g(x) from the graph. f(x) is the red parabola and g(x) is the blue line.
2. Evaluate f(0) by finding the y-coordinate of the point where the red parabola intersects the y-axis.
3. Evaluate g(0) by finding the y-coordinate of the point where the blue line intersects the y-axis.
4. Calculate (f \cdot g)(0) by multiplying the values of f(0) and g(0).
5. Verify the calculations by checking the graph for accuracy of the y-intercepts at x = 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, (ƒg)(0) means we first evaluate g(0) and then use that result as the input for the function f. Understanding how to perform this operation is crucial for solving the problem.

Evaluating Functions from Graphs

To evaluate functions from their graphs, one must identify the corresponding y-values for given x-values. For instance, to find g(0), locate x = 0 on the graph of g(x) and read the y-coordinate. This skill is essential for accurately determining the values needed for function composition.

Interpreting Graphs

Interpreting graphs involves understanding the visual representation of functions, including their shapes, intersections, and behaviors. The graph provided shows a quadratic function f(x) and a linear function g(x), which helps in visualizing how these functions interact and aids in evaluating expressions like (ƒg)(0).