Evaluate the following piecewise functions.
\(1)\) Find \(f(3)\) if
\(\,\,\,f(x) = \begin{cases}
x+2 & \text{if } x\lt 3 \\
-x+2 & \text{if }x\geq 3
\end{cases}\)
The answer is \(-(3)+2=-1\)
\(2)\) Find \(f(3)\) if
\(\,\,\,f(x) = \begin{cases}
x+1 & \text{if } x\leq 3 \\
-x+5 & \text{if }x\gt 4
\end{cases}\)
The answer is \((3)+1=4\)
\(3)\) Find \(f(5)\) if
\(\,\,\,f(x) = \begin{cases}
x^2-9 & \text{if } x\lt 4 \\
x-5 & \text{if }x\geq 4
\end{cases}\)
The answer is \((5)-5=0\)
\(4)\) Find \(f(0)\) if
\(\,\,\,f(x) = \begin{cases}
5x & \text{if } x\lt 0 \\
5 & \text{if }x\geq 0
\end{cases}\)
The answer is \(5\)
\(5)\) Find \(f(-1)\) if
\(\,\,\,f(x) = \begin{cases}
-2x-4 & \text{if } x\lt 0 \\
x+1 & \text{if }x\geq 0
\end{cases}\)
The answer is \(-2(-1)+4=-2\)
\(6)\) Find \(f(2)\) if
\(\,\,\,f(x) = \begin{cases}
x+3 & \text{if } x\lt 2 \\
-x+2 & \text{if }x\geq 2
\end{cases}\)
The answer is \(-(2)+2=0\)
\(7)\) Find \(f(4)\) if
\(\,\,\,f(x) = \begin{cases}
3x+3 & \text{if } x\leq 2 \\
-2x+8 & \text{if }x\geq 5
\end{cases}\)
The answer is undefined
\(8)\) Find \(f(3)\) if
\(\,\,\,f(x) = \begin{cases}
x^2-6 & \text{if } x\lt 4 \\
5 & \text{if }x\geq 4
\end{cases}\)
The answer is \((3)^2-6=3\)
\(9)\) Find \(f(3)\) if
\(\,\,\,f(x) = \begin{cases}
x & \text{if } x\lt -3 \\
4 & \text{if } -3\leq x\leq 4 \\
-2 & \text{if }x\gt 4
\end{cases}\)
The answer is \(4\)
\(10)\) Find \(f(3)\) if
\(\,\,\,f(x) = \begin{cases}
x^2 & \text{if } x\lt 3 \\
-x+1 & \text{if }x\geq 3
\end{cases}\)
The answer is \(-(3)+1=-2\)
\(11)\) Find \(f(1)\) if
\(\,\,\,f(x) = \begin{cases}
5 & \text{if } x\lt 0 \\
3 & \text{if }x\geq 4
\end{cases}\)
The answer is undefined
\(12)\) Find \(f(6)\) if
\(\,\,\,f(x) = \begin{cases}
x+9 & \text{if } x\lt -3 \\
x^2-6 & \text{if } -3\leq x\leq 4 \\
-x & \text{if }x\gt 4
\end{cases}\)
The answer is \(-(6)=-6\)
\(13)\) Find \(f(-2)\) if
\(\,\,\,f(x) = \begin{cases}
x^2-8 & \text{if } x\lt 0 \\
7 & \text{if }x\geq 0
\end{cases}\)
The answer is \((-2)^2-8=-4\)
\(14)\) Find \(f(1)\) if
\(\,\,\,f(x) = \begin{cases}
6 & \text{if } x\lt -4 \\
x+1 & \text{if } -4\leq x\lt 4 \\
-x+2 & \text{if }x\geq 4
\end{cases}\)
The answer is \((1)+1=2\)
\(15)\) Find \(f(7)\) if
\(\,\,\,f(x) = \begin{cases}
x+2 & \text{if } x\geq 4 \\
x^2 & \text{if }x\lt 4
\end{cases}\)
The answer is \((7)+2=9\)
\(16)\) Find \(f(3)\) if
\(\,\,\,f(x) = \begin{cases}
-x+5 & \text{if } x\gt 4 \\
x & \text{if }x\leq 3
\end{cases}\)
The answer is \( (3)=3 \)
\(17)\) Find \(f(8)\) if
\(\,\,\,f(x) = \begin{cases}
-x+5 & \text{if } x\gt 4 \\
x & \text{if }x\leq 3
\end{cases}\)
The answer is \((-8)+5\)
\(18)\) Find \(f(6)\) if
\(\,\,\,f(x) = \begin{cases}
-x+5 & \text{if } x\leq 4 \\
x-3 & \text{if } 4\lt x \lt 6 \\
x & \text{if }x\geq 6
\end{cases}\)
The answer is \( (6)=6 \)
\(19)\) Find \(f(5)\) if
\(\,\,\,f(x) = \begin{cases}
-x+5 & \text{if } x\leq 4 \\
x-3 & \text{if } 4\lt x \lt 6 \\
x & \text{if }x\geq 6
\end{cases}\)
The answer is \( (5)-3=2 \)
\(20)\) Find \(f(-1)\) if
\(\,\,\,f(x) = \begin{cases}
\frac{x^2+6x+5}{x+1} & \text{if } x \neq -1 \\
5 & \text{if }x = -1
\end{cases}\)
The answer is \( (5)=5 \)
\(21)\) Find \(f(7)\) if
\(\,\,\,f(x) = \begin{cases}
2x^2 & \text{if } x\leq 2 \\
6x-3 & \text{if } 2\lt x \lt 4 \\
x^2+1 & \text{if }x\geq 4
\end{cases}\)
The answer is \( (7)^2+1=50 \)
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