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

Verified step by step guidance

1. Identify the value of x for which you need to evaluate the expression (f - g)(1). Here, x = 1.
2. Find the value of f(1) by locating x = 1 on the horizontal axis and then moving vertically to the orange curve representing f(x). Read the corresponding y-value.
3. Find the value of g(1) by locating x = 1 on the horizontal axis and then moving vertically to the blue line representing g(x). Read the corresponding y-value.
4. Use the definition of the difference of functions: (f - g)(1) = f(1) - g(1).
5. Subtract the value of g(1) from f(1) to get the result of (f - g)(1).

Key Concepts

Function Evaluation

Function evaluation involves finding the output value of a function for a given input. For example, to evaluate f(1), locate x = 1 on the graph and find the corresponding y-value on the curve of f(x). This process is essential for understanding how functions behave at specific points.

Function Operations (Subtraction)

Function operations combine two functions to create a new function. In subtraction, (f - g)(x) means subtracting the value of g(x) from f(x) for the same input x. Evaluating (f - g)(1) requires finding f(1) and g(1) separately, then subtracting g(1) from f(1).

Interpreting Graphs of Functions

Interpreting graphs involves reading values from the plotted curves of functions. By identifying points on the graph at a specific x-value, you can determine the corresponding y-values for f(x) and g(x). This skill is crucial for evaluating expressions like (f - g)(1) using graphical data.