Evaluate the function at the indicated values. f(x)={ x^2+2 x if x ≤-1 x if -

step 1 In this question we have given here the function f x is equal to x squared plus 2 x and the cond

Evaluate the function at the indicated values. f(x)={ ...

Evaluate the function at the indicated values.
$$f(x)=\left\{\begin{array}{ll}
x^{2}+2 x & \text { if } x \leq-1 \\
x & \text { if }-1<x \leq 1 \\
-1 & \text { if } x>1
\end{array}\right.$$
$$f(-4), f\left(-\frac{3}{2}\right), f(-1), f(0), f(25)$$

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Key Concepts

Piecewise Functions

A piecewise function is defined by different expressions for different parts of its domain. This type of function uses separate formulas which apply to designated intervals or conditions, allowing a single function to exhibit varied behavior across its range.

Domain Conditions

Domain conditions refer to the specific intervals or inequalities that determine which expression of a piecewise function should be used for a particular input value. Correctly identifying these conditions is crucial for accurately evaluating the function at any given point.

Function Evaluation

Function evaluation involves substituting the given value into the appropriate part of the function's definition according to its domain conditions. When working with a piecewise function, it is important to first identify the correct interval for the input before performing the substitution.

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