Question

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

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

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.