Answered

What are the domain, range, and asymptote of h(x) = (1.4)^x + 5?

Adomain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
Bdomain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5
Cdomain: {x | x > –5}; range: {y | y is a real number}; asymptote: y = –5
Ddomain: {x | x is a real number}; range: {y | y > –5}; asymptote: y = –5

Verified Answer :

LammettHash

\((1.4)^x\) is always positive for any real \(x\), so by itself the range would be \(y>0\), but \((1.4)^x+5\) adds 5 to every number in that original range. This means the actual range would be all positive numbers greater than 5, or \(\{y~|~y>5\}\).

Conveniently, only (B) has this as an option for the range, so this must be the answer. (The other two properties check out, since \(x\) can indeed be any real number, while \(\displaystyle\lim_{x\to\-\infty}h(x)=5\), so \(y=5\) is indeed a horizontal asymptote of \(h(x)\).)

Using exponential function concepts, it is found that the correct option that gives the domain, range, and asymptote of h(x) is:

A. domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5

What is an exponential function?

An exponential function is modeled by:

\(y = b^x + c\)

  • The domain is all real numbers.
  • The range is y > c.
  • The asymptote is y = c.

In this problem, the function is:

\(y = (1.4)^x + 5\)

Hence c = 5, and the option A is correct.

You can learn more about exponential function concepts at https://brainly.com/question/25537936

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