91Ó°ÊÓ

Evaluating functions involves finding the value of a function at a specific input. This means substituting the given input value into the function and simplifying the expression. For example, in the exercise, the function is given by: \br\br\br\br\br\brbrbrbr $$f(x)=|x-2|+|x+1|-5$$ \br\br When evaluating functions, replacing the variable (\brx\br) with each provided input value is crucial. Each step involves \br simplifying the expression step by step, especially focusing on evaluating absolute values as seen in the given exercise. \br\br \br For instance, in \br step 1, we were asked to \brfind \br\bf(-3)\br:
Substitute \br x=-3\br into the function: \br\bd(-3) =|-3-2|+|-3+1|-5\br\br\br\br Simplify the absolute values: \br\br|-5|+|-2|-5=5+2-5=2\br, so \bf(-3)br= br2 \br.\br\br Applying the same process to other values like \br-2, 0, and 4\br, you get the desired output as shown in the solution steps.

This meticulous substitution and calculation help students understand the function's behavior at given inputs. It demonstrates how to handle expressions involving absolute values effectively.

Piecewise functions are functions defined by multiple sub-functions, each applying to a specific interval of the main function's domain. In the given exercise, the absolute value function can be seen as a piecewise function. The absolute value function \br can be written in a piecewise form: \br\br\br\br $$|x| = \begin{cases} x & \text{if } x \text{ is non-negative}\ -x & \text{if } x \text{ is negative} \br\br=br-2f\br<=> \br \br\bd(-2)- test