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What are the domain, range, and asymptote of h(x) = 2x + 4? domain: {x | x > 0}; range: {y | y is a real number}; asymptote: y = 0 domain: {x | x > –4}; range: {y | y is a real number}; asymptote: y = –4 domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = 0 domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = –4

Verified Answer :

frika

Consider the function \(y=2^{x+4}.\) First, note that parent function \(y=2^x\) has

  • the domain \(x\in (-\infty,\infty)\) (all real numbers);
  • the range \(y>0\) (all positive real numbers);
  • the asymptote \(y=0\) (horizontal line).

The graph of the function \(y=2^{x+4}\) can be obtained from the parent function using translation 4 units to the left. This translation doesn't change the domain, the range and the asymptote of the parent function.

Answer: correct choice is C

Answer:  

Option 3 is correct.

\(D=(-\infty,\infty)[x|x\in {R}]\)

\(R=(0,\infty)[y|y>0]\)

y=0 is the asymptote.  

Step-by-step explanation:

Given : The function \(h(x) = 2^{x + 4}\)

To find : The domain, range, and asymptote of the given function.

Solution :

The given function \(h(x) = 2^{x + 4}\) is an exponential function.

Domain is where the function is defined.

Therefore, \(D=(-\infty,\infty)[x|x\in {R}]\)

The range is the set of values that correspond with the domain.

At x tends to \(-\infty\) function tends to zero.

At x tends to \(\infty\) function tends to  \(\infty\)

Therefore, \(R=(0,\infty)[y|y>0]\)

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is  y=0.

Therefore, Option 3 is correct.

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