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3 years ago

What’s the graph function f(x) =4(1.5)^x

Mathematics

1 answer:

WARRIOR [948]3 years ago

6 0

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.

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