# What are the domain, range, and asymptote of h(x) = (0.5)x – 9?

## Answers

[tex](1.4)^x[/tex] is always positive for any real [tex]x[/tex], so by itself the range would be [tex]y0[/tex], but [tex](1.4)^x+5[/tex] adds 5 to every number in that original range. This means the actual range would be all positive numbers greater than 5, or [tex]\{y~|~y5\}[/tex].

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

[tex]What are the domain, range, and asymptote of h(x) = (1.4)^x + 5? a. domain: {x | x is a real numbe[/tex]

Option 3 is correct.

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

[tex]R=(0,\infty)[y|y0][/tex]

y=0 is the asymptote.

Step-by-step explanation:

Given : The function [tex]h(x) = 2^{x + 4}[/tex]

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

Solution :

The given function [tex]h(x) = 2^{x + 4}[/tex] is an exponential function.

Domain is where the function is defined.

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

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

At x tends to [tex]-\infty[/tex] function tends to zero.

At x tends to [tex]\infty[/tex] function tends to [tex]\infty[/tex]

Therefore, [tex]R=(0,\infty)[y|y0][/tex]

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is y=0.

Therefore, Option 3 is correct.

115

step-by-step explanation:

A.Domain:{x\x is a real number }

Range:{y\y>5}

Asymptote :y=5

Step-by-step explanation:

We are given that a function

[tex]h(x)=(1.4)^x+5[/tex]

We have to find the domain, range and asymptote of h(x).

It is exponential function therefore, it is defined for all values of x.

Hence, domain of h(x)={x| x is a real number}

Substitute x=0 then we get

[tex]h(0)=(1.4)^0+5=1+5=6[/tex]

(a^0=1)

Hence, range of h(x)={y|y>5}

For exponential function,

Horizontal asymptote:[tex]a^x\rightarrow 0[/tex] when [tex]x\rightarrow-\infty[/tex]

Apply limit [tex]x\rightarrow-\infty[/tex]

[tex]\lim_{x\rightarrow-\infty}h(x)=\lim_{x\rightarrow-\infty}(1.4)^x+5=0+5=5[/tex]

[tex]e^{-\infty}=0[/tex]

[tex]\lim_{x\rightarrow \infty}(1.4)^x+5=\infty[/tex]

Hence, the horizontal asymptote y=5.

a

Step-by-step explanation:

Consider the function [tex]y=2^{x+4}.[/tex] First, note that parent function [tex]y=2^x[/tex] has

the domain [tex]x\in (-\infty,\infty)[/tex] (all real numbers);the range [tex]y0[/tex] (all positive real numbers);the asymptote [tex]y=0[/tex] (horizontal line).The graph of the function [tex]y=2^{x+4}[/tex] 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.

correct choice is C

Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Step-by-step explanation:

Given : [tex]h(x)=(0.5)^x-9[/tex]

To find : What are the domain, range, and asymptote of h(x) ?

Solution :

Domain of the function is where the function is defined

The given function [tex]h(x)=(0.5)^x-9[/tex] is an exponential function

So, the domain of the function is,

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

i.e, The set of all real numbers.

Range is the set of value that corresponds to the domain.

Let [tex]y=(0.5)^x-9[/tex]

If [tex]x\rightarrow \infty , y\rightarrow -9[/tex]

If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]

So, The range of the function is

[tex]R=(-9,\infty) , y|y-9[/tex]

The asymptote of the function,

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is when

[tex]x\rightarrow \infty[/tex]

[tex]y=(0.5)^\infty-9[/tex]

[tex]y=-9[/tex]

Therefore, Option 4 is correct.

Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Step-by-step explanation:

The domain of a function is the set for which the function is defined. Our function is the function [tex]h(x) = 6x-4[/tex]. This function is defined regardless of the value of x, so it is defined for every real value of x. That is, it's domain is the set {x|x is a real number}.

The range of the function is the set of all possible values that the function might take, that is {y|y=6x-4}. Recall that every real number y could be written of the form y=6x-4 for a particular x. So the range of the function is the set {y|y is a real number}.

Note that as x gets bigger, the value of 6x-4 gets also bigger, then it doesn't approach any particular number. Note also that as x approaches - infinity, the value of 6x-4 approaches also - infinity. In this case, we don't have any horizontal asymptote. Since the function is defined for every real number, it doesn't have any vertical asymptote. Since h is a linear function, it cannot have any oblique asymptote, then h doesn't have any asymptote.

Among the choices provided above the domain, range, and asymptote of h(x) = (0.5)x – 9 is the below:

domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

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The answer is A because I got it right