Use the given function:f(x) = {x+3,−x3,if 0≤x<2if 2≤x≤5Find the value of f(3)

The given function \( f(x) \) is defined piecewise as follows:

\[
f(x) = 
\begin{cases} 
x + 3 & \text{if } 0 \leq x < 2 \\
-x^3 & \text{if } 2 \leq x \leq 5 
\end{cases}
\]

We are asked to find \( f(3) \).

1. Since \( 3 \) is within the interval \( 2 \leq x \leq 5 \), we use the second part of the piecewise function:
\[
f(x) = -x^3
\]

2. Substituting \( x = 3 \) into this expression:
\[
f(3) = -(3)^3 = -27
\]

Thus, \( f(3) = -27 \).

Would you like further details or have any questions? Here are some related questions for further practice:

1. What is the value of \( f(1) \)?
2. What is the value of \( f(2) \)?
3. What is the domain of the function \( f(x) \)?
4. Is \( f(x) \) continuous at \( x = 2 \)?
5. Can you graph the function \( f(x) \)?

**Tip:** When dealing with piecewise functions, always check which part of the function applies to the given input based on its domain.

Use the given function: f(x) = {x + 3, if 0 ≤ x < 2; -x^3, if 2 ≤ x ≤ 5. Find the value of f(3).

Learn how to evaluate a piecewise function with two parts: f(x) = x + 3 for 0 ≤ x < 2, and f(x) = -x^3 for 2 ≤ x ≤ 5. This step-by-step guide explains how to find f(3), using the correct portion of the function based on the input's domain. Suitable for Grades 9-11.

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