Translations of Exponential Functions — Quiz

Question 6 • Algebra: Concepts and Connections

What are the domain, range, and asymptote of h of x is equal to 2 raised to the x plus 4 power ?

Answer

domain: start set x such that x is a real number end set ; range: start set y such that y is greater than 0 end set ; asymptote: y is equal to negative 4

domain: start set x such that x is greater than 0 end set ; range: start set y such that y is a real number end set ; asymptote: y is equal to 0

domain: start set x such that x is greater than negative 4 end set ; range: start set y such that y is a real number end set ; asymptote: y is equal to negative 4

domain: start set x such that x is a real number end set ; range: start set y such that y is greater than 0 end set ; asymptote: y is equal to 0

Explanation

For h(x) = 2^(x + 4), the exponent can be any real number, so the domain is all real numbers. A positive base raised to any real power is always positive, so the range is y > 0. As x decreases without bound, h(x) approaches 0, making y = 0 the horizontal asymptote; this matches choice B.

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