Use the graph to evaluate each expression. See Example 3(a).
(ƒ/g)(2)

Verified step by step guidance

1. Identify the value of the functions f(x) and g(x) at x = 2 by locating the point where x = 2 on the x-axis and reading the corresponding y-values from the graph for both f(x) (red curve) and g(x) (blue line).
2. Write down the values you found: f(2) and g(2). These are the y-values of the red and blue graphs at x = 2, respectively.
3. Recall that the expression (ƒ/g)(2) means the value of the function f(x) divided by the value of the function g(x) at x = 2, which can be written as \(\frac{f(2)}{g(2)}\).
4. Substitute the values of f(2) and g(2) into the expression \(\frac{f(2)}{g(2)}\) to set up the division.
5. Make sure to check that g(2) is not zero before dividing, as division by zero is undefined.

Key Concepts

Function Evaluation

Function evaluation involves finding the output value of a function for a given input. For example, to evaluate f(2), locate x = 2 on the graph and find the corresponding y-value on the curve of f(x). This process applies to any function and is essential for understanding function behavior at specific points.

Function Division (Quotient of Functions)

The division of two functions, denoted (f/g)(x), means dividing the value of f(x) by g(x) at the same input x. It is important to ensure g(x) ≠ 0 to avoid undefined expressions. This concept helps in combining functions and analyzing their ratios.

Reading Graphs to Determine Function Values

Reading graphs accurately is crucial for evaluating functions visually. Identify the input value on the x-axis, then trace vertically to the function curve to find the output on the y-axis. This skill allows you to estimate function values when algebraic expressions are not given.