Use the following table to find each value, if possible. X Y 1 Y2 -3 -4 1

step 1 In this problem, we need to evaluate the function Y1, composed of Y2 at a value of negative 3. L

Use the following table to find each value, if possible. ...

Use the following table to find each value, if possible. $$\begin{array}{|c|c|c|}\hline X & {Y 1} & {Y_{2}} \\ \hline-3 & {-4} & {1} \\ {-2} & {-1} & {-2} \\ {-1} & {2} & {-3} \\ {0} & {5} & {-2} \\ {1} & {8} & {1} \\ {2} & {11} & {6} \\ {3} & {14} & {11} \\ \hline {\text {X} =} \\ \hline \end{array}$$ $$\left(y_{1} \circ y_{2}\right)(-3)$$

Use the following table to find each value, if possible.
$$\begin{array}{|c|c|c|}\hline X & {Y 1} & {Y_{2}} \\
\hline-3 & {-4} & {1} \\
{-2} & {-1} & {-2} \\
{-1} & {2} & {-3} \\
{0} & {5} & {-2} \\
{1} & {8} & {1} \\
{2} & {11} & {6} \\
{3} & {14} & {11} \\
\hline {\text {X} =} \\ \hline \end{array}$$
$$\left(y_{1} \circ y_{2}\right)(-3)$$

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Key Concepts

Function Composition

Function composition involves applying one function to the result of another, written as (f ? g)(x) = f(g(x)). It is a fundamental concept in mathematics that allows the creation of more complex functions by combining simpler ones. This process emphasizes the order of operations where the output of the inner function serves as the input to the outer function.

Interpreting Function Tables

Function tables provide a convenient way to display pairs of inputs and corresponding outputs for a function. They help in quickly identifying the value of a function for a given input without the need for an explicit formula, making them particularly useful when evaluating functions that are part of compositions.

Evaluation of Composite Functions

Evaluating composite functions requires a two-step process: first, identify the output of the inner function using its table or definition, and then use that output as the input for the outer function. This sequential approach ensures that the composition is properly calculated, adhering to the function composition concept.

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