Question

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

Answer 1

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 2

Option 3 is correct.

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

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

y=0 is the asymptote.

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.