+25 1) Let \(f(x) = \left\{ \begin{array}{cl} 3x & \text{if } x < 3, \\ 3^x & \text{if } x \ge 3. \end{array} \right.\) Find \(f(2) + f(3) + f(4).\)
2) Let \(f(x) = \left\{ \begin{array}{cl} -2x & \text{if } x < 0, \\ \frac{x}{2} & \text{if } x \ge 0. \end{array} \right.\) Find the range of f(x) in interval notation.
3) Find the area of the region that lies below the graph of y = 3 - |x - 1| but above the -axis.
+9481 1)
\(f(x) = \left\{ \begin{array}{cl} 3x & \text{if } x < 3, \\ 3^x & \text{if } x \ge 3. \end{array} \right.\)
Let's find f(2)
2 < 3 so we use f(x) = 3x
f(2) = 3(2)
f(2) = 6
Let's find f(3)
3 ≥ 3 so we use f(x) = 3x
f(3) = 33
f(3) = 27
Let's find f(4)
4 ≥ 3 so we use f(x) = 3x
f(4) = . . .? Can you figure this one out?
+9481 2)
\(f(x) = \left\{ \begin{array}{cl} -2x & \text{if } x < 0, \\ \frac{x}{2} & \text{if } x \ge 0. \end{array} \right.\)
Let y = f(x) so we can say that...
The range includes the smallest possible y value to the biggest possible y value.
A graph might help:
The smallest possible y value is 0
There isn't a biggest possible y value because we can always find a bigger one, so we say it's ∞
So the range is [0, ∞)
