Question

use technology to find points and then graph the function $y = 2^{x + 2} - 4$, following the instructions below.

equation of asymptote:
$y = \boxed{-4}$

plot at least four points with integer coordinates that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x-values

Pick integer x-values, e.g., \( x = -2, -1, 0, 1 \).

Step2: Calculate y for \( x = -2 \)

Substitute \( x = -2 \) into \( y = 2^{x+2} - 4 \):
\( y = 2^{-2+2} - 4 = 2^0 - 4 = 1 - 4 = -3 \).
Point: \( (-2, -3) \).

Step3: Calculate y for \( x = -1 \)

Substitute \( x = -1 \):
\( y = 2^{-1+2} - 4 = 2^1 - 4 = 2 - 4 = -2 \).
Point: \( (-1, -2) \).

Step4: Calculate y for \( x = 0 \)

Substitute \( x = 0 \):
\( y = 2^{0+2} - 4 = 2^2 - 4 = 4 - 4 = 0 \).
Point: \( (0, 0) \).

Step5: Calculate y for \( x = 1 \)

Substitute \( x = 1 \):
\( y = 2^{1+2} - 4 = 2^3 - 4 = 8 - 4 = 4 \).
Point: \( (1, 4) \).

Answer:

Points: \((-2, -3)\), \((-1, -2)\), \((0, 0)\), \((1, 4)\) (and asymptote \( y = -4 \)).