Answer:
See below
Explanation:
Here's one way to sketch the graph of a function.
Step 1. Find any zeroes.
(a) y-intercept
y = 2(4)^x Let x = 0
= 2(4)⁰
= 2 × 1
= 2
We have a point at (0,2).
(b) x-intercept
y = 2(4)^x Let y = 0
0 = 2(4)^x Divide each side by 2
0 = (4)^x Take the log of each side
log0 = xlog4
log(0) is undefined. There is no x-intercept.
Step 2. Identify any asymptotes
y = 2(4)^x
y can never be negative, so the x-axis is an asymptote.
Step 3. Calculate and plot a few points
Here's a table of a few points.
x y
-3 0.0
-2 0.1
-1 0.5
0 2
1 8
2 32
3 128
Step 4. Check the end behaviour.
y = 2(4)^x
As x ⟶ ∞, y ⟶ ∞.
As x ⟶ -∞, y ⟶ 0
Step 5. Draw a smooth line through the points.
Your graph should look something like the one below.