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.

Suspect May 18, 2019

#1**+2 **

**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) = 3^{x}

f(3) = 3^{3}

**f(3) = 27**

Let's find f(4)

4 ≥ 3 so we use f(x) = 3^{x}

f(4) = . . .? Can you figure this one out?

hectictar May 18, 2019

#2**+3 **

**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, ∞)

hectictar May 18, 2019