A. Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have the same domain of [tex](9, +\infty)[/tex].
In this question we must analyze the domain, range, x-intercepts and increase intervals:
[tex]Dom \{f(x)\} = \mathbb{R}[/tex]
[tex]Dom \{g(x)\} = \mathbb{R}[/tex]
Both functions are continuous.
[tex]Ran \left\{f(x)\right\} = (3.875, +\infty)[/tex]
[tex]Ran \{g(x)\} = (-5, +\infty)[/tex]
[tex]f(x):[/tex] [tex](x,y) = \emptyset[/tex]
[tex]g(x):[/tex] [tex](x,y) = (2.322, 0)[/tex]
[tex]f(x):[/tex] According to the graph, [tex]f(x)[/tex] increase over the interval of [tex](3.875, + \infty)[/tex].
[tex]g(x) :[/tex] According to the graph, [tex]g(x)[/tex] increase over the interval of [tex]\mathbb{R}[/tex]
After a quick analysis, we conclude that option A offer the best approximation to characteristics of both functions. [tex]\blacksquare[/tex]
The statement presents mistakes and is poorly formatted. Correct form is:
Given a polynomial function [tex]f(x) = 2\cdot x^{2}-3\cdot x + 5[/tex] and an exponential function [tex]g(x) = 2^{x}-5[/tex]. What key features do [tex]f(x)[/tex] and [tex]g(x)[/tex] have in common?
A. Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have the same domain of [tex](9, +\infty)[/tex].
B. Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have the same range of [tex](-\infty, 0][/tex].
C. Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have the same x-intercept of [tex](2,0)[/tex].
D. Both [tex]f(x)[/tex] and [tex]g(x)[/tex] increase over the interval of [tex](-4, +\infty)[/tex].
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