Graph the function f(x)=(3/2)^x. How do i go about graphing by hand. Also i have 2 find asymptotes.?

Answer 1

The graph of f(x) = b^x for any b > 1 has these properties:

f(x) > 0 for all x
The graph goes through the points (0,1) and (1, b)
It is increasing for all x
It is concave up everywhere
There are no critical points and no inflection points (if you know calculus)
f(x) → ∞ as x → ∞
f(x) → 0 as x → -∞ (because f(-x) = 1/f(x)), so the (negative) x-axis is a horizontal asymptote
(There are no other asymptotes)

I would plot for x=0, ±1, ±3, and ±5. Note that f(-x)=1/f(x); so, for example, f(-3) = 1/f(3) = 1/3.375 ≈ 0.296

Use larger values of x if you want to make it clearer how fast f(x) eventually increases with x.