Exponential Functions — Test

Question 15 • Mathematics I

What are the domain, range, and asymptote of h of x is equal to 6 to the x th power minus 4 ?

Answer

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

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

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

Explanation

The exponential expression 6^x is defined for every real number x, so the domain is all real numbers. Since 6^x is always positive, subtracting 4 makes h(x) greater than −4, giving the range y > −4. As x decreases without bound, 6^x approaches 0, so the horizontal asymptote is y = −4. Choice D gives all three correctly.

AI-written and checked against the verified answer.

More from this Course

Test

Test

Test