Question

use technology to find points and then graph the function $y = 2^{x+2} - 1$, following the instructions below.
plot at least four points with integer coordinates that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x=-2

Substitute \( x = -2 \) into \( y = 2^{x + 2}-1 \), we get \( y = 2^{-2 + 2}-1 = 2^{0}-1 = 1 - 1 = 0 \). So the point is \((-2, 0)\).

Step2: Choose x=-1

Substitute \( x = -1 \) into \( y = 2^{x + 2}-1 \), we get \( y = 2^{-1 + 2}-1 = 2^{1}-1 = 2 - 1 = 1 \). So the point is \((-1, 1)\).

Step3: Choose x=0

Substitute \( x = 0 \) into \( y = 2^{x + 2}-1 \), we get \( y = 2^{0 + 2}-1 = 2^{2}-1 = 4 - 1 = 3 \). So the point is \((0, 3)\).

Step4: Choose x=1

Substitute \( x = 1 \) into \( y = 2^{x + 2}-1 \), we get \( y = 2^{1 + 2}-1 = 2^{3}-1 = 8 - 1 = 7 \). So the point is \((1, 7)\).

Answer:

The four points with integer coordinates are \((-2, 0)\), \((-1, 1)\), \((0, 3)\), \((1, 7)\) (you can plot these points on the given graph).