Use the graph to evaluate each expression. See Example 3(a).
(ƒ-g)(-1)

Verified step by step guidance

1. Understand that (ƒ - g)(-1) means you need to find the value of ƒ(-1) and g(-1) from the graph, then subtract g(-1) from ƒ(-1).
2. Locate the point where x = -1 on the x-axis and find the corresponding y-value on the red curve (ƒ(x)) to determine ƒ(-1).
3. Next, locate the point where x = -1 on the x-axis and find the corresponding y-value on the blue line (g(x)) to determine g(-1).
4. Write the expression for the difference: (ƒ - g)(-1) = ƒ(-1) - g(-1).
5. Substitute the values you found for ƒ(-1) and g(-1) into the expression and simplify to find the result.

Key Concepts

Function Notation and Evaluation

Function notation, such as f(x) and g(x), represents the output of a function for a given input x. To evaluate a function at a specific value, substitute the input into the function and find the corresponding output on the graph or from the equation.

Operations on Functions (Addition and Subtraction)

Operations like (f - g)(x) involve subtracting the output of g(x) from f(x) for the same input x. This means evaluating both functions at x and then subtracting their values to find the result.

Reading Values from a Graph

To evaluate functions from a graph, locate the input value on the x-axis, then find the corresponding y-values for each function by tracing vertically to the graph lines. These y-values represent the function outputs needed for calculations.