Use the tables for ƒ and g to evaluate each expression. (g∘ƒ)(-2)

Verified step by step guidance

1. Identify the function ƒ(-2) from the table for ƒ. This value will be used as the input for the function g.
2. Substitute the value of ƒ(-2) into the function g. This means you will look up the value of g at the point that corresponds to ƒ(-2).
3. Evaluate g at this new input value. This will give you the result of (g∘ƒ)(-2).
4. The notation (g∘ƒ)(-2) represents the composition of g and ƒ, evaluated at -2. This means you first apply ƒ to -2, and then apply g to the result of ƒ(-2).
5. Write down the final value obtained from evaluating g at the point ƒ(-2). This is the value of (g∘ƒ)(-2).

Key Concepts

Function Composition

Function composition is the process of combining two functions, where the output of one function becomes the input of another. In this case, (g∘ƒ)(-2) means we first evaluate the function ƒ at -2, and then take that result and use it as the input for the function g. Understanding how to properly execute this sequence is crucial for solving the problem.

Evaluating Functions

Evaluating functions involves substituting a specific value into a function to find its output. For example, if ƒ(x) is defined in a table, to find ƒ(-2), you would look up the value corresponding to -2 in that table. This step is essential in function composition, as the output of the first function directly influences the input of the second function.

Understanding Function Notation

Function notation is a way to represent functions and their operations clearly. The notation g∘ƒ indicates the composition of functions g and ƒ, while ƒ(-2) and g(y) denote the evaluation of these functions at specific points. Familiarity with this notation helps in interpreting and manipulating expressions involving multiple functions.