The correct option is Option C: As x approaches positive Infinity, h(t) approaches positive infinity.
What is the exponential function?
The exponential function is a function where the base is raised exponent times where the exponent is an input variable and the base is a constant.
For example: f(x)= aˣ
Similarly here given in the question,
the function is h(x)= [tex]2^{x-5[/tex]
the domain of this function is real number R i.e (-∞,∞)
The range of the function is real numbers greater than 0.
So when x approaches to negative infinity,
[tex]\lim_{x \to- \infty} h(x)[/tex]
= [tex]\lim_{x \to- \infty} 2^{x-5[/tex]
= 2^(-∞-5)
= 2^(-∞)
= 1/2^∞
=0
So, As x approaches negative infinity, function h(x) approaches 0.
Then when x approaches to positive infinity,
[tex]\lim_{x \to \infty} h(x)[/tex]
= [tex]\lim_{x \to \infty} 2^{x-5[/tex]
= 2^(∞-5)
= 2^(∞)
= ∞
So, As x approaches positive Infinity, h(t) approaches positive infinity.
By checking all the options there is only one option that matches the above conclusion.
Therefore the correct option is Option C: As x approaches positive Infinity, h(t) approaches positive infinity.
Learn more about exponential function
here: https://brainly.com/question/2456547
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