Answer:
See below.
Step-by-step explanation:
Step 1. Find any zeroes.
(a) y-intercept
y = 4(1.5)^x Let x = 0
= 4(1.5)⁰
= 4 × 1
= 4
We have a point at (0,4).
(b) x-intercept
y = 4(1.5)^x Let y = 0
0 = 4(1.5)^x Divide each side by 4
0 = (1.5)^x Take the log of each side
log0 = xlog1.5
log(0) is undefined. There is no x-intercept.
Step 2. Identify any asymptotes
y = 4(1.5)^x
y can never be negative, so the x-axis is an asymptote.
Step 3. Plug in and plot a few points
Here's a table of a few points.
x y
-6 0.4
-4 0.8
-2 1.8
-1 2.7
0 4.0
1 6.0
2 9.0
4 20.3
6 45.6
Step 4. Check the end behaviour.
y = 4(1.5)^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.
