Question

use technology to find points and then graph the function $y = 2^x - 4$, following the instructions below.
equation of asymptote:
$y = -4$
plot at least four points with integer coordinates that fit on the axes below. click a point to delete it.

Explanation:

Step1: Recall exponential function transformation

The parent function is \( y = 2^x \), which has a horizontal asymptote at \( y = 0 \). For \( y = 2^x - 4 \), it's a vertical shift down by 4 units, so the asymptote is \( y=-4 \), which matches the given boxed value.

Step2: Find integer coordinate points

• For \( x = 0 \): \( y = 2^0 - 4 = 1 - 4 = -3 \), so point \( (0, -3) \).
• For \( x = 1 \): \( y = 2^1 - 4 = 2 - 4 = -2 \), so point \( (1, -2) \).
• For \( x = 2 \): \( y = 2^2 - 4 = 4 - 4 = 0 \), so point \( (2, 0) \).
• For \( x = 3 \): \( y = 2^3 - 4 = 8 - 4 = 4 \), so point \( (3, 4) \).
• For \( x = -1 \): \( y = 2^{-1} - 4=\frac{1}{2}-4 = -\frac{7}{2} \) (not integer, skip).
• For \( x = -2 \): \( y = 2^{-2} - 4=\frac{1}{4}-4 = -\frac{15}{4} \) (not integer, skip).

Answer:

The asymptote equation is \( y = -4 \), and four points with integer coordinates are \( (0, -3) \), \( (1, -2) \), \( (2, 0) \), \( (3, 4) \) (you can plot these on the graph). The asymptote is \( y = -4 \).