Question

use technology to find points and then graph the function $y = 2^x - 2$, following the instructions below. done plotting points plot at least four points with integer coordinates that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose integer x-values

Let's pick x = -1, 0, 1, 2. These are simple integers to calculate y for.

Step2: Calculate y for x = -1

Substitute x = -1 into \( y = 2^x - 2 \). So \( y = 2^{-1} - 2 = \frac{1}{2} - 2 = -\frac{3}{2} \). Wait, but we need integer coordinates. Maybe x = 1? Wait, no, let's check x = 0: \( y = 2^0 - 2 = 1 - 2 = -1 \). x = 1: \( y = 2^1 - 2 = 2 - 2 = 0 \). x = 2: \( y = 2^2 - 2 = 4 - 2 = 2 \). x = 3: \( y = 2^3 - 2 = 8 - 2 = 6 \). Wait, maybe better x values. Let's try x = -1: \( 2^{-1} = 0.5 \), not integer. x = 0: y = -1 (integer). x = 1: y = 0 (integer). x = 2: y = 2 (integer). x = 3: y = 6 (integer). So the points are (0, -1), (1, 0), (2, 2), (3, 6). Wait, but let's check x = -2: \( 2^{-2} - 2 = 0.25 - 2 = -1.75 \), not integer. So the four points with integer coordinates are (0, -1), (1, 0), (2, 2), (3, 6). To plot them, for (0, -1): x=0, y=-1. (1, 0): x=1, y=0. (2, 2): x=2, y=2. (3, 6): x=3, y=6.

Answer:

The four points with integer coordinates are (0, -1), (1, 0), (2, 2), (3, 6) (you can plot these on the graph).