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**Unformatted text preview: **6-3: Exponential Functions
Exponential function is a function in the form f(x) = ax where a is a positive real number and a
≠ 1. The domain of f is the set of all real numbers. The laws of exponents for real (irrational)
exponents are the same as those for integer and rational exponents. Irrational exponents are
F+ 1 I
1
truncated to a finite number of digits, so that ar≈ ax. The number e is the number that G n J
HK
approaches as n→∞.
n f(x) = ax Range x-intercept y-intercept a>1 (0, ∞ ) None (0, 1) Horizontal
asymptote
x-axis as x →-∞ 0<a<1 (0, ∞ ) None (0, 1) x-axis as x →∞ Characteristic
Increasing,
one-to-one
Decreasing
one-to-one Passes
through
(0, 1) (1, a)
(0, 1) (1, a) Approximate to three decimal places: 1. 5 3 ≈ 16.242 2. 2e ≈ 6.581 Graph the following exponential functions; state the domain, range, and any horizontal asymptote:
3. x y=2
y = 2x+2;
y = 2x – 2 1
FI
y= G =2
HJ
2K
x 4. -x 5. y = ex y = 2-x-2; y = -ex; y = 2-x + 2 y = 2 - ex 6. Atmospheric pressure p measured in mm of mercury is related to the number of
km h above sea level by the formula p = 760e-0.145h. Find the pressure at a height
of 2 km and at a height of 10 km. p =760e-0.145(2) ≈ 568.68 p =760e-0.145(10) ≈ 178.27 Exponential Equations: If au = av, then u = v.
1− 2 x 7. 5 1
=
5 1
8. 2 1− x =4 9. ()
e4 x 2 ⋅ e x = e 12 ...

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