Question

Given that the domain is all real numbers, what is the limit of the range for the function ƒ(x) = 4^2x - 100?

Answer 1

[ -100, ∞ ). as X decreases f of x approaches -100 asymptotically as X increases f of x increases without bound

Answer 2

Answer:

The limit of the range is y>-100.

Step-by-step explanation:

Given : The domain is all real numbers, for the function $f(x) = 4^{2x} - 100$

To find : what is the limit of the range for the function?

Solution :

The function we have given is an exponential function.

The domain of the function $f(x) = 4^{2x} - 100$  is all real number.

i.e, $D=(-\infty,\infty),[x|x\in\mathbb{R}]$

Range is defined as the set of value that corresponds with the domain.

Taking, $x\rightarrow\infty$

Function approaches to -100

Taking, $x\rightarrow -\infty$

Function approaches to $\infty$

Therefore, The range of the function is defined as

$R=(-100,\infty),[y|y>-100]$

So, The limit of the range is y>-100.