What us the exact value of cos(5pi/6)?
2 answers:
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Answer:
See below.
Step-by-step explanation:
Step 1. Find any zeroes.
(a) <em>y-intercept </em>
y = 4(1.5)^x Let x = 0
= 4(1.5)⁰
= 4 × 1
= 4
We have a <em>point at (0,4)</em>.
(b) <em>x-intercept </em>
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 <em>no x-intercept. </em>
Step 2. Identify any asymptotes
y<em> </em>= 4(1.5)^x
y can never be negative, so the <em>x-axis is an asymptot</em>e.
Step 3. Plug in and plot a few points
Here's a table of a few points.
<u> x y </u>
-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.
