Translations of Exponential Functions — Quiz

Question 3 • Algebra: Concepts and Connections

What are the domain, range, and asymptote of h of x is equal to 1 point 4 to the x th power plus 5 ?

Answer

domain: start set x such that x is a real number end set ; range: start set y such that y is greater than negative 5 end set ; asymptote: y is equal to negative 5

domain: start set x such that x is greater than 5 end set ; range: start set y such that y is a real number end set ; asymptote: y is equal to 5

domain: start set x such that x is greater than negative 5 end set ; range: start set y such that y is a real number end set ; asymptote: y is equal to negative 5

domain: start set x such that x i s a real number end set ; range: start set y such that y is greater than 5 end set ; asymptote: y is equal to 5

Explanation

The function is h(x) = 1.4^x + 5. Since an exponential expression is defined for every real x, the domain is all real numbers. Also, 1.4^x is always positive, so h(x) is always greater than 5; as x decreases without bound, 1.4^x approaches 0, making y = 5 the horizontal asymptote. Thus, the correct choice is D.

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