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domain range continuousThe student is expected to determine the domain and range of exponential functions of the form f(x) = ab x and represent the domain and range using inequalities.

DOMAIN AND RANGE OF EXPONENTIAL FUNCTIONS

Domain

Range A.?A

EXAMPLES

EXAMPLE :

STEP ?

The possible range is h(x) > 4.

f(x) = 2 x + 2

Asymptote:

y = 2, a > 0

Range does not include the

asymptote. All real numbers greater than ________. g(x) = -(2) x - 3 - 1

Asymptote:

y = -1, a < 0

Range does not include the

asymptote. All real numbers less than ________.

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ALGEBRA ? TEKS COMPANION GUIDE

STEP ?ȱ ȱȱȱȱȱȱȱȱęȱȱȱȱȱȱǯ

The horizontal asymptote is y = 4.

STEP ?

The domain of

h(x) is all real numbers.

The range of

h(x) is all real numbers greater than 4, or h(x) > 4. EXAMPLE ?:ȱ Ĵȱȱ ȱ ȱ ȱ ǯȱ ȱ

STEP ?

Both variables are limited to non-negative

numbers ( y-axis and Quadrant I) in this situation.

STEP ?

The domain of the function in this situation

is x ≥ 0.

STEP ?

The range of the function in this situation is

0 < 5

YOU TRY IT!

© Cosenza & Associates, LLCEXPONENTIAL FUNCTIONS AND EQUATIONS 185

EXAMPLE :

STEP ?

STEP ?

-2, not inclusive, is the lower limit of the domain.

8, not inclusive, is the upper limit of the range.

STEP ?ȱ ȱȱȱȱěȱȱȱȱȱǯ -8, not inclusive, is the lower limit of the range. STEP ?ȱ ȱȱȱȱȱȱǰȱǰȱȱȱȱǯȱȱȱȱȱ -2 < x STEP ?ȱ ȱȱȱȱȱȱǰȱǰȱȱȱȱǯȱȱȱȱȱ -8 < y < 8

PRACTICE

1. 2. 3.

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