Question

use technology to find points and then graph the function $y = 2^{x+5} - 10$, following the instructions below.

done plotting points

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

Explanation:

Step1: Choose integer x-values

Select integer values for \( x \) (e.g., \( x = -5, -4, -3, -2, -1 \)) to make calculations easier.

Step2: Calculate y for \( x = -5 \)

Substitute \( x = -5 \) into \( y = 2^{x + 5}-10 \):
\( y = 2^{-5 + 5}-10 = 2^{0}-10 = 1 - 10 = -9 \).
Point: \( (-5, -9) \).

Step3: Calculate y for \( x = -4 \)

Substitute \( x = -4 \):
\( y = 2^{-4 + 5}-10 = 2^{1}-10 = 2 - 10 = -8 \).
Point: \( (-4, -8) \).

Step4: Calculate y for \( x = -3 \)

Substitute \( x = -3 \):
\( y = 2^{-3 + 5}-10 = 2^{2}-10 = 4 - 10 = -6 \).
Point: \( (-3, -6) \).

Step5: Calculate y for \( x = -2 \)

Substitute \( x = -2 \):
\( y = 2^{-2 + 5}-10 = 2^{3}-10 = 8 - 10 = -2 \).
Point: \( (-2, -2) \).

Step6: Calculate y for \( x = -1 \)

Substitute \( x = -1 \):
\( y = 2^{-1 + 5}-10 = 2^{4}-10 = 16 - 10 = 6 \).
Point: \( (-1, 6) \).

(These points can be plotted on the given coordinate system. The graph of \( y = 2^{x + 5}-10 \) is an exponential curve shifted left by 5 units and down by 10 units from the parent function \( y = 2^{x} \).)

Answer:

Points with integer coordinates: \((-5, -9)\), \((-4, -8)\), \((-3, -6)\), \((-2, -2)\), \((-1, 6)\) (and more can be calculated similarly for graphing).