Question

Function h is a transformation of the parent exponential function. Which statement is true about this function? h(x) = 2^(x-5)
As x approaches negative infinity, h(r) approaches negative infinity.
As x approaches positive infinity, h(t) approaches 0.
As x approaches positive Infinity, h(t) approaches positive infinity.
As x approaches negative infinity, h(a) approaches positive infinity.​

Answer 1

Answer: As x approaches positive infinity, h(x) approaches positive infinity

Step-by-step explanation:

Answer 2

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)= $2^{x-5$

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,

$\lim_{x \to- \infty} h(x)$

= $\lim_{x \to- \infty} 2^{x-5$

= 2^(-∞-5)

= 2^(-∞)

= 1/2^∞

=0

So, As x approaches negative infinity, function h(x) approaches 0.

Then when x approaches to positive infinity,

$\lim_{x \to \infty} h(x)$

= $\lim_{x \to \infty} 2^{x-5$

= 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

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