Use the graphs of f and g to solve Exercises 83–90.
Find(g/f)(3)

Verified step by step guidance

1. Identify the value of g(3) from the graph of g(x).
2. Identify the value of f(3) from the graph of f(x).
3. Ensure that f(3) is not equal to zero to avoid division by zero.
4. Calculate (g/f)(3) by dividing g(3) by f(3).
5. Express the result as (g/f)(3) = g(3)/f(3).

Key Concepts

Function Notation

Function notation is a way to represent functions in mathematics, typically using symbols like f(x) and g(x). Here, f and g are functions, and x is the input variable. Understanding function notation is crucial for interpreting and manipulating functions, especially when performing operations like addition, subtraction, multiplication, or division.

Graph Interpretation

Interpreting graphs involves analyzing the visual representation of functions to extract information about their behavior. In this case, the graphs of f(x) and g(x) provide insights into their values at specific points, such as x = 3. This skill is essential for solving problems that require evaluating functions based on their graphical representations.

Division of Functions

The division of functions, denoted as (g/f)(x), represents the quotient of two functions g(x) and f(x). To find (g/f)(3), one must evaluate g(3) and f(3) from their respective graphs and then compute the ratio g(3)/f(3). Understanding how to perform operations on functions is fundamental in algebra, particularly when dealing with composite or rational functions.