Translations of Exponential Functions — Quiz

Question 7 • Algebra: Concepts and Connections

What are the domain, range, and asymptote of h of x is equal to 0 point 5 to the x th power minus 9 ?

Answer

domain: start set x such that x is greater than negative 9 end set ; range: start set y such that y is a real number end set ; asymptote: y is equal to negative 9

domain: start set x such that x is a real number end set ; range: start set y such that y is greater than negative 9 end set ; asymptote: y is equal to negative 9

domain: start set x such that x is a real number end set ; range: start set y such that y is greater than 9 end set ; asymptote: y is equal to 9

domain: start set x such that x is greater than 9 end set ; range: start set y such that y is a rea l number end set ; asymptote: y is equal to 9

Explanation

The exponential expression 0.5^x is defined for every real number x, so the domain is all real numbers. Since 0.5^x is always positive, subtracting 9 makes h(x) always greater than -9. As x increases, 0.5^x approaches 0, so the graph approaches the horizontal asymptote y = -9. This matches choice C.

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