Question

Consider the following piecewise definition of the function f.
\(f(x) =   \begin{cases}   3-x,\,\,\,if & \quad x≤0\\     x^2 +2,\,if & \quad x≥0  \end{cases}\)
Evaluate f(-3).

• A. 6
• B. 0
• C. 11
• D. -7

Answer 1

The Correct Option is A

To evaluate the function \(f(-3)\) using the given piecewise definition, we first need to determine which part of the function applies to \(x = -3\).

The function \(f(x)\) is defined as:

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

Since \(-3 \leq 0\), we use the first piece of the function: \(f(x) = 3-x\).

Substitute \(x = -3\) into the expression:

\[f(-3) = 3 - (-3) = 3 + 3 = 6\]

Thus, the value of \(f(-3)\) is 6.